Exhibit 5.1

[Letterhead of Burns & Levinson LLP]

Board of Directors

Biostage, Inc.

84 October Hill Road, Suite 11

Holliston, MA 01746

Ladies and Gentlemen:

We have acted as counsel to Biostage, Inc., a Delaware corporation (the “Company”), in connection with the preparation of a Registration Statement on Form S-1 (Registration No. 333-215410) (the “Registration Statement”) filed by the Company with the U.S. Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), on January 3, 2017, as amended on February 3, 2017 and February 7, 2017, with respect to the offer and sale of (a) 7,936,508 shares (the “Common Shares”) of the Company’s common stock, par value $0.01 per share (the “Common Stock”), (b) 2,000 shares (the “Preferred Shares”) of the Company’s Series C Convertible Preferred Stock, par value $0.01 per share (the “Series C Preferred Stock”), which are convertible into an aggregate of 2,645,503 shares of the Company’s Common Stock (the “Conversion Shares”) (c) warrants (the “Warrants”) to purchase an aggregate of 10,582,011 shares of Common Stock (the “Warrant Shares”), (d) warrants (the “Representative’s Warrants”) to purchase an aggregate of 529,101 shares of Common Stock (the “Representative’s Warrant Shares”) and (e) the associated preferred stock purchase rights (the “Rights”) to be issued pursuant to the Shareholder Rights Agreement, dated as of October 31, 2008, between the Company and Registrar and Transfer Company, as amended by Amendment No. 1 dated February 12, 2015 (as amended, the “Rights Agreement”) by and between the Company and Computershare Trust Company, N.C., as successor to Registrar and Transfer Company (the “Rights Agent”). The Common Shares, Preferred Shares, Conversion Shares, Warrants, Warrant Shares, Representatives’ Warrants, Representatives’ Warrant Shares and Rights are referred to herein collectively as the “Securities.”

The Securities are to be sold by the Company pursuant to an engagement letter entered into by and between the Company and H.C. Wainwright& Co., LLC, as placement agent (the “Placement Agent”), dated as of January 3, 2017, as amended on February 7, 2017 (as amended, the “Engagement Letter”), which have been filed as Exhibit 10.31 and Exhibit 10.32 to the Registration Statement

Biostage, Inc.

February 7, 2017

Page 2

In connection with this opinion, we have examined and relied upon the Registration Statement and the Prospectus, the Company’s Amended and Restated Certificate of Incorporation, the Company’s Amended and Restated By-Laws, the Engagement Letter, the Warrants, the Representative’s Warrants, the Certificate of Designation designating the Series C Preferred Stock, the securities purchase agreement pursuant to which certain of the Securities are to be sold (together with the Engagement Letter, the “Agreements”), and such instruments, documents, certificates and records that we have deemed relevant and necessary for the basis of our opinion hereinafter expressed. In such examination, we have assumed: (i) the authenticity of original documents and the genuineness of all signatures; (ii) the conformity to the originals of all documents submitted to us as copies; (iii) the truth, accuracy and completeness of the information, representations and warranties contained in the records, documents, instruments and certificates we have reviewed; and (iv) the due execution and delivery of all documents where due execution and delivery are a prerequisite to the effectiveness thereof.

In rendering this opinion, we have also assumed that the Rights Agreement was duly authorized, executed and delivered by the Rights Agent and that the members of the Company’s Board of Directors (the “Board”) acted in a manner consistent with their fiduciary duties as required under applicable law in adopting the Rights Agreement. With respect to the Rights, our opinion does not address the determination a court of competent jurisdiction may make regarding whether the Board would be required to redeem or terminate, or take other action with respect to, the Rights at some future time based on the facts and circumstances existing at that time. This opinion addresses the Rights and the Rights Agreement in their entirety and not any particular provision of the Rights or the Rights Agreement, and it should be understood that it is not settled whether the invalidity of any particular provision of a rights agreement or of purchase rights issued thereunder would result in invalidating such rights in their entirety. The Rights exist by virtue of and are subject to the Rights Agreement and the terms and conditions thereof, and it should be understood that the Rights Agreement and the Rights may be terminated or amended at the Company’s option.

Based upon the foregoing, we are of the opinion that:

1. The Common Shares, when issued and sold in accordance with the terms set forth in the Agreements and the Registration Statement against payment therefor, will be duly authorized, validly issued, fully paid and non-assessable.

2. The Preferred Shares, when issued and sold in accordance with the terms set forth in the Agreements and the Registration Statement against payment therefor, will be duly authorized, validly issued, fully paid and non-assessable.

Biostage, Inc.

February 7, 2017

Page 3

3. Provided that the Warrants have been duly executed and delivered by the Company and duly delivered to the purchasers thereof against payment therefor, then the Warrants, when issued and sold in accordance with the terms set forth in the Agreements and the Registration Statement, will constitute the valid and legally binding obligations of the Company.

4. Provided that the Representative’s Warrants have been duly executed and delivered by the Company and duly delivered to the Placement Agent, then the Representative’s Warrants, when issued and sold in accordance with the terms set forth in the Agreements and the Registration Statement, will constitute the valid and legally binding obligations of the Company.

5. The Conversion Shares have been duly authorized for issuance and, when issued upon the conversion of the Preferred Shares in accordance with the terms thereof, will be validly issued, fully paid and non-assessable.

6. The Warrant Shares have been duly authorized for issuance and, when issued and delivered against payment therefor in accordance with the provisions of the Warrants, including the payment of the exercise price therefor, will be validly issued, fully paid and non-assessable.

7. The Representative’s Warrant Shares have been duly authorized for issuance and, when issued and delivered against payment therefor in accordance with the provisions of the Warrants, including the payment of the exercise price therefor, will be validly issued, fully paid and non-assessable.

8. The Rights, when issued and sold in accordance with the terms set forth in the Agreements, the Rights Agreement and the Registration Statement, will constitute the valid and legally binding obligations of the Company.

This opinion is limited to the General Corporate Laws of the State of Delaware, the laws of the State of New York and the United States federal laws, and we express no opinion with respect to the laws of any other jurisdiction. No opinion is expressed herein with respect to the qualification of the Shares under the securities or blue sky laws of any state or foreign jurisdiction.

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Biostage, Inc.

February 7, 2017

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We hereby consent to the filing of this opinion as Exhibit 5.1 to the Registration Statement and to the reference to this firm under the caption “Legal Matters” in the Registration Statement.

In giving this consent, we do not admit that we are within the category of persons whose consent is required by Section 7 of the Securities Act or the rules and regulations promulgated thereunder by the Commission.