Exhibit 3.1

RESTATED CERTIFICATE OF INCORPORATION

OF

AMEDICA CORPORATION

(Pursuant to Sections 242 and 245 of the

General Corporation Law of the State of Delaware)

Amedica Corporation, a corporation organized and existing under the laws of the State of Delaware (the “Corporation”), hereby certifies as follows:

The Corporation filed a Certificate of Incorporation with the Secretary of State of the State of Delaware was December 10, 1996 under the name Amedica Corp. A Restated Certificate of Incorporation of the Corporation was filed on October 25, 2004 (the “Base Restated Certificate”), and the Base Restated Certificate was amended by (a) a Certificate of Designation for Series C Convertible Preferred Stock filed on February 24, 2006, (b) a Certificate of Designation for Series D Convertible Preferred Stock filed on April 16, 2007, (c) Certificates of Amendment respectively filed on July 26, 2007 and November 1, 2007, (d) a Certificate of Increase of Series D Convertible Preferred Stock filed on December 21, 2007, (e) a Certificate of Amendment filed on March 1, 2010, (f) a Certificate of Designation for Series E Convertible Preferred Stock filed March 19, 2010, (g) Certificates of Designation of Series A-1 Convertible Preferred Stock, Series B-1 Convertible Preferred Stock, Series C-1 Convertible Preferred Stock and Series D-1 Convertible Preferred Stock filed on March 19, 2010, (h) a Certificate of Amendment filed on March 19, 2010, (i) a Certificate of Increase of Series D-1 Convertible Preferred Stock filed on March 24, 2010, (j) a Certificate of Decrease of the Series A Convertible Preferred Stock, Series B Convertible Preferred Stock, Series C Convertible Preferred Stock and Series D Convertible Preferred Stock filed on March 25, 2010, (k) a Certificate of Increase of Series E Convertible Preferred Stock filed on September 20, 2010, (l) a Certificate of Increase of Series C Convertible Preferred Stock filed May 10, 2012, (m) a Certificate of Increase of Series D Convertible Preferred Stock and a Certificate of Decrease of Series E Convertible Preferred Stock, each filed on December 14, 2012, (n) a Certificate of Designation of Series F Convertible Preferred Stock filed on December 14, 2012, (o) a Certificate of Amendment filed on August 27, 2013, (p) a Certificate of Increase of Series F Convertible Preferred Stock filed on August 27, 2013, (q) a Certificate of Amendment filed on February 10, 2014, (r) a Certificate of Amendment filed on February 10, 2014, and (s) a Certificate of Amendment filed on February 11, 2014.

This Restated Certificate of Incorporation restates, integrates and further amends the Base Restated Certificate, as heretofore amended.

This Restated Certificate of Incorporation was duly adopted by written consent of the directors and stockholders of the Corporation in accordance with the applicable provisions of Sections 228, 242 and 245 of the General Corporation Law of the State of Delaware.

The text of the Corporation’s Certificate of Incorporation, as amended, is hereby further amended and restated to read in full as follows:

RESTATED CERTIFICATE OF INCORPORATION

OF

AMEDICA CORPORATION

FIRST: The name of the corporation is Amedica Corporation (the “Corporation”).

SECOND: The address of the registered office of the Corporation in the State of Delaware is 1209 Orange Street, Wilmington, Delaware 19810, County of New Castle. The name of its registered agent at such address is The Corporation Trust Company.

THIRD: The purpose of the Corporation is to engage in any lawful act or activity or carry on any business for which corporations may be organized under the Delaware General Corporation Law or any successor statute.

FOURTH:

A. Designation and Number of Shares.

The total number of shares of all classes of stock which the Corporation shall have the authority to issue is Three Hundred Eighty Million (380,000,000) shares, consisting of Two Hundred Fifty Million (250,000,000) shares of common stock, par value $0.01 per share (the “Common Stock”), and One Hundred Thirty Million (130,000,000) shares of preferred stock, par value $0.01 per share (the “Preferred Stock”).

The number of authorized shares of Common Stock or Preferred Stock may be increased or decreased (but not below the number of shares thereof then outstanding) by the affirmative vote of the holders of a majority of the voting power of all of the then-outstanding shares of capital stock of the Corporation entitled to vote thereon, without a vote of the holders of the Preferred Stock, or of any series thereof, unless a vote of any such holders is required pursuant to the terms of any Preferred Stock designation.

B. Preferred Stock.

1. Shares of Preferred Stock may be issued in one or more series at such time or times and for such consideration as the Board of Directors of the Corporation (the “Board of Directors”) may determine.

2. Authority is hereby expressly granted to the Board of Directors to fix from time to time, by resolution or resolutions providing for the establishment and/or issuance of any series of Preferred Stock, the designation and number of the shares of such series and the powers, preferences and rights of such series, and the qualifications, limitations or restrictions thereof, to the fullest extent such authority may be conferred upon the Board of Directors under the Delaware General Corporation Law. Without limiting the generality of the foregoing, the resolutions providing for issuance of any series of Preferred Stock may provide that such series

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shall be superior or rank equally or be junior to the Preferred Stock of any other series to the extent permitted by law.

C. Common Stock.

1. Dividends. Dividends may be declared and paid on the Common Stock from funds lawfully available therefor if, as and when determined by the Board of Directors in their sole discretion, subject to provisions of law, any provision of this Restated Certificate of Incorporation, as amended from time to time, and subject to the relative rights and preferences of any shares of Preferred Stock authorized, issued and outstanding hereunder. The term “Restated Certificate of Incorporation” as used herein shall mean the Restated Certificate of Incorporation of the Corporation as amended from time to time.

2. Voting. The holders of the Common Stock are entitled to one vote for each share held; provided, however, that, except as otherwise required by law, holders of Common Stock shall not be entitled to vote on any amendment to this Restated Certificate of Incorporation (including any certificate of designation relating to Preferred Stock) that relates solely to the terms of one or more outstanding series of Preferred Stock if the holders of such affected series are entitled, either separately or together as a class with the holders of one or more other such series, to vote thereon by law or pursuant to this Restated Certificate of Incorporation (including any certificate of designation relating to Preferred Stock).

FIFTH: The following provisions are inserted for the management of the business and the conduct of the affairs of the Corporation, and for further definition, limitation and regulation of the powers of the Corporation and of its directors and stockholders:

A. The business and affairs of the Corporation shall be managed by or under the direction of the Board of Directors. In addition to the powers and authority expressly conferred upon them by statute or by this Restated Certificate of Incorporation or the Bylaws of the Corporation as in effect from time to time, the directors are hereby empowered to exercise all such powers and do all such acts and things as may be exercised or done by the Corporation.

B. The directors of the Corporation need not be elected by written ballot unless the Bylaws so provide.

C. Subject to the rights of the holders of any series of Preferred Stock then outstanding, any action required or permitted to be taken by the stockholders of the Corporation may be effected only at a duly called annual or special meeting of stockholders of the Corporation and not by written consent.

D. Special meetings of the stockholders may only be called by the Board of Directors acting pursuant to a resolution adopted by a majority of the Whole Board. For the purposes of this Restated Certificate of Incorporation, the term “Whole Board” shall mean the total number of authorized directors whether or not there exist any vacancies in previously authorized directorships. Business transacted at any special meeting of stockholders shall be limited to matters relating to the purpose or purposes stated in the notice of meeting.

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SIXTH:

A. Subject to the rights of the holders of shares of any series of Preferred Stock then outstanding to elect additional directors under specified circumstances, the number of directors shall be fixed from time to time exclusively by the Board of Directors pursuant to a resolution adopted by a majority of the Whole Board.

B. The directors, other than those who may be elected by the holders of shares of any series of Preferred Stock under specified circumstances, shall be divided into three classes, with the term of office of the first class to expire at the first annual meeting of stockholders following the initial classification of directors, the term of office of the second class to expire at the second annual meeting of stockholders following the initial classification of directors, and the term of office of the third class to expire at the third annual meeting of stockholders following the initial classification of directors. At each annual meeting of stockholders, directors elected to succeed those directors whose terms expire, other than directors elected by the holders of any series of Preferred Stock under specified circumstances, shall be elected for a term of office to expire at the third succeeding annual meeting of stockholders after their election and until their successors are duly elected and qualified. The Board of Directors is authorized to assign members of the Board already in office to such classes as it may determine at the time the classification of the Board of Directors pursuant to this Restated Certificate of Incorporation becomes effective.

C. Subject to the rights of the holders of any series of Preferred Stock then outstanding, newly created directorships resulting from any increase in the authorized number of directors or any vacancies in the Board of Directors resulting from death, resignation, retirement, disqualification, removal from office or other cause shall, unless otherwise required by law or by resolution of the Board of Directors, be filled only by a majority vote of the directors then in office even though less than a quorum, or by a sole remaining director, and not by stockholders, and directors so chosen shall serve for a term expiring at the annual meeting of stockholders at which the term of office of the class to which they have been chosen expires or until such director’s successor shall have been duly elected and qualified. No decrease in the authorized number of directors shall shorten the term of any incumbent director.

D. Advance notice of stockholder nominations for the election of directors and of business to be brought by stockholders before any meeting of the stockholders of the Corporation shall be given in the manner provided in the Bylaws of the Corporation.

E. Subject to the rights of the holders of any series of Preferred Stock then outstanding, any director, or the entire Board of Directors, may be removed from office at any time only for cause and only by the affirmative vote of the holders of at least eighty percent (80%) of the voting power of all of the then-outstanding shares of capital stock of the Corporation entitled to vote at an election of directors, voting together as a single class.

SEVENTH: The Board of Directors is expressly empowered to adopt, amend or repeal Bylaws of the Corporation. Any adoption, amendment or repeal of the Bylaws of the Corporation by the Board of Directors shall require the approval of a majority of the Whole

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Board. The stockholders shall also have power to adopt, amend or repeal the Bylaws of the Corporation; provided, that in addition to any vote of the holders of any class or series of stock of the Corporation required by law or by this Restated Certificate of Incorporation, the affirmative vote of the holders of at least eighty percent (80%) of the voting power of all of the then outstanding shares of the capital stock of the Corporation entitled to vote generally in the election of directors, voting together as a single class, shall be required for the stockholders to adopt, amend or repeal any provision of the Bylaws of the Corporation.

EIGHTH:

A. Each person who was or is made a party or is threatened to be made a party to or is otherwise involved (including, without limitation, as a witness) in any action, suit or proceeding, whether civil, criminal, administrative or investigative, by reason of the fact that he is or was a director or an officer of the Corporation or is or was serving at the request of the Corporation as a director, officer, or trustee of another corporation, or of a partnership, joint venture, trust or other enterprise, including service with respect to an employee benefit plan (hereinafter an “Indemnitee”), whether the basis of such proceeding is alleged action in an official capacity as a director, officer or trustee or in any other capacity while serving as a director, officer or trustee, shall be indemnified and held harmless by the Corporation to the fullest extent permitted by the Delaware General Corporation Law, as the same exists or may hereafter be amended (but, in the case of any such amendment, only to the extent that such amendment permits the Corporation to provide broader indemnification rights than such law permitted the Corporation to provide prior to such amendment), against all expense, liability and loss (including attorneys’ fees, judgments, fines, ERISA excise taxes or penalties and amounts paid in settlement) reasonably incurred or suffered by such Indemnitee in connection therewith; provided, however, that, except as provided in Paragraph C of this Article EIGHTH with respect to proceedings to enforce rights to indemnification or an advancement of expenses or as otherwise required by law, the Corporation shall not be required to indemnify or advance expenses to any such Indemnitee in connection with a proceeding (or part thereof) initiated by such Indemnitee unless such proceeding (or part thereof) was authorized by the Board of Directors of the Corporation.

B. In addition to the right to indemnification conferred in Paragraph A of this Article EIGHTH, an Indemnitee shall also have the right to be paid by the Corporation the expenses (including attorney’s fees) incurred in defending any such proceeding in advance of its final disposition; provided, however, that, if the Delaware General Corporation Law requires, an advancement of expenses incurred by an Indemnitee in his capacity as a director or officer (and not in any other capacity in which service was or is rendered by such Indemnitee, including, without limitation, service to an employee benefit plan) shall be made only upon delivery to the Corporation of an undertaking, by or on behalf of such Indemnitee, to repay all amounts so advanced if it shall ultimately be determined by final judicial decision from which there is no further right to appeal that such Indemnitee is not entitled to be indemnified for such expenses under this Paragraph B or otherwise.

C. If a claim under Paragraph A or B of this Article EIGHTH is not paid in full by the Corporation within sixty (60) days after a written claim has been received by the Corporation, except in the case of a claim for an advancement of expenses, in which case the applicable period

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shall be twenty (20) days, the Indemnitee may at any time thereafter bring suit against the Corporation to recover the unpaid amount of the claim. If successful in whole or in part in any such suit, or in a suit brought by the Corporation to recover an advancement of expenses pursuant to the terms of an undertaking, the Indemnitee shall also be entitled to be paid the expenses of prosecuting or defending such suit. In (i) any suit brought by the Indemnitee to enforce a right to indemnification hereunder (but not in a suit brought by the Indemnitee to enforce a right to an advancement of expenses) it shall be a defense that, and (ii) in any suit brought by the Corporation to recover an advancement of expenses pursuant to the terms of an undertaking, the Corporation shall be entitled to recover such expenses upon a final adjudication that, the Indemnitee has not met any applicable standard for indemnification set forth in the Delaware General Corporation Law. Neither the failure of the Corporation (including its directors who are not parties to such action, a committee of such directors, independent legal counsel, or its stockholders) to have made a determination prior to the commencement of such suit that indemnification of the Indemnitee is proper in the circumstances because the Indemnitee has met the applicable standard of conduct set forth in the Delaware General Corporation Law, nor an actual determination by the Corporation (including its directors who are not parties to such action, a committee of such directors, independent legal counsel, or its stockholders) that the Indemnitee has not met such applicable standard of conduct, shall create a presumption that the Indemnitee has not met the applicable standard of conduct or, in the case of such a suit brought by the Indemnitee, be a defense to such suit. In any suit brought by the Indemnitee to enforce a right to indemnification or to an advancement of expenses hereunder, or brought by the Corporation to recover an advancement of expenses pursuant to the terms of an undertaking, the burden of proving that the Indemnitee is not entitled to be indemnified, or to such advancement of expenses, under this Article EIGHTH or otherwise shall be on the Corporation.

D. The rights to indemnification and to the advancement of expenses conferred in this Article EIGHTH shall not be exclusive of any other right which any person may have or hereafter acquire under any statute, the Corporation’s Certificate of Incorporation as amended from time to time, the Corporation’s Bylaws, any agreement, any vote of stockholders or disinterested directors or otherwise.

E. The Corporation may maintain insurance, at its expense, to protect itself and any director, officer, employee or agent of the Corporation or another corporation, partnership, joint venture, trust or other enterprise against any expense, liability or loss, whether or not the Corporation would have the power to indemnify such person against such expense, liability or loss under the Delaware General Corporation Law.

F. The Corporation may, to the extent authorized from time to time by the Board of Directors, grant rights to indemnification and to the advancement of expenses to any employee or agent of the Corporation to the fullest extent of the provisions of this Article EIGHTH with respect to the indemnification and advancement of expenses of directors and officers of the Corporation.

G. The rights conferred upon Indemnitees in this Article EIGHTH shall be contract rights and such rights shall continue as to an Indemnitee who has ceased to be a director, officer, employee or agent and shall inure to the benefit of the Indemnitee’s heirs, executors and administrators. Any amendment, alteration or repeal of this Article EIGHTH that adversely affects

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any right of an Indemnitee or its successors shall be prospective only and shall not limit or eliminate any such right with respect to any proceeding involving any occurrence or alleged occurrence of any action or omission to act that took place prior to any such amendment, alteration or repeal.

H. If any word, clause, provision or provisions of this Article EIGHTH shall be held to be invalid, illegal or unenforceable for any reason whatsoever: (i) the validity, legality and enforceability of the remaining provisions of this Article EIGHTH (including, without limitation, each portion of any section of this Article EIGHTH containing any such provision held to be invalid, illegal or unenforceable, that is not itself held to be invalid, illegal or unenforceable) shall not in any way be affected or impaired thereby; and (ii) to the fullest extent possible, the provisions of this Article EIGHTH (including, without limitation, each such portion of any section of this Article EIGHTH containing any such provision held to be invalid, illegal or unenforceable) shall be construed so as to give effect to the intent manifested by the provision held invalid, illegal or unenforceable.

NINTH: No director shall be personally liable to the Corporation or its stockholders for any monetary damages for breaches of fiduciary duty as a director; provided that this provision shall not eliminate or limit the liability of a director, to the extent that such liability is imposed by applicable law, (i) for any breach of the director’s duty of loyalty to the Corporation or its stockholders; (ii) for acts or omissions not in good faith or which involve intentional misconduct or a knowing violation of law; (iii) under Section 174 or successor provisions of the Delaware General Corporation Law; or (iv) for any transaction from which the director derived an improper personal benefit. No amendment to or repeal of this provision shall apply to or have any effect on the liability or alleged liability of any director for or with respect to any acts or omissions of such director occurring prior to such amendment or repeal. If the Delaware General Corporation Law is amended to authorize corporate action further eliminating or limiting the personal liability of directors, then the liability of a director of the Corporation shall be eliminated or limited to the fullest extent permitted by the Delaware General Corporation Law, as so amended. All references in this Article NINTH to a director shall also be deemed to refer to any such director acting in his or her capacity as a Continuing Director (as defined in Article ELEVENTH).

TENTH: The Corporation reserves the right to amend or repeal any provision contained in this Restated Certificate of Incorporation in the manner prescribed by the Delaware General Corporation Law and all rights conferred upon stockholders are granted subject to this reservation, provided that in addition to the vote of the holders of any class or series of stock of the Corporation required by law or by this Restated Certificate of Incorporation, the affirmative vote of the holders of shares of voting stock of the Corporation representing at least eighty percent (80%) of the voting power of all of the then outstanding shares of the capital stock of the Corporation entitled to vote generally in the election of directors, voting together as a single class, shall be required to amend, alter or repeal, or adopt any provision inconsistent with, Articles FIFTH, SIXTH, SEVENTH, EIGHTH, NINTH, this Article TENTH and Article ELEVENTH of this Restated Certificate of Incorporation.

ELEVENTH: The Board of Directors is expressly authorized to cause the Corporation to issue rights pursuant to Section 157 of the Delaware General Corporation Law and, in that

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connection, to enter into any agreements necessary or convenient for such issuance, and to enter into other agreements necessary and convenient to the conduct of the business of the Corporation. Any such agreement may include provisions limiting, in certain circumstances, the ability of the Board of Directors of the Corporation to redeem the securities issued pursuant thereto or to take other action thereunder or in connection therewith unless there is a specified number or percentage of Continuing Directors then in office. Pursuant to Section 141(a) of the Delaware General Corporation Law, the Continuing Directors shall have the power and authority to make all decisions and determinations, and exercise or perform such other acts that any such agreement provides that such Continuing Directors shall make, exercise or perform. For purposes of this Article ELEVENTH and any such agreement, the term, “Continuing Directors,” shall mean (1) those directors who were members of the Board of Directors of the Corporation at the time the Corporation entered into such agreement and any director who subsequently becomes a member of the Board of Directors, if such director’s nomination for election to the Board of Directors is recommended or approved by the majority vote of the Continuing Directors then in office or (2) such members of the Board of Directors designated in, or in the manner provided in, such agreement as Continuing Directors.

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IN WITNESS WHEREOF, this Restated Certificate of Incorporation, which restates and integrates and further amends the provisions of the Certificate of Incorporation, as amended, of the Corporation, and which has been duly adopted in accordance with Sections 228, 242 and 245 of the Delaware General Corporation Law, has been duly executed by its duly authorized Secretary on February 19, 2014.

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