Exhibit 5.1

 Thompson Hine LLP

March 2, 2020

Vaxart, Inc.

290 Utah Ave., Suite 200

South San Francisco, CA 94080

Ladies and Gentlemen:

We have acted as counsel to Vaxart, Inc., a Delaware corporation (the “Company”) in connection with the offering of an aggregate of 4,000,000 shares (each, a “Share”) of common stock, $0.10 par value per share, of the Company (the “Common Stock”) and warrants (the “Warrants”) to purchase 2,000,000 shares of Common Stock pursuant to the Securities Purchase Agreement, dated February 27, 2020 (the “Purchase Agreement”), by and among the Company and each purchaser identified on the signature pages thereto. In addition, the Company is issuing warrants to purchase up to 280,000 shares of Common Stock to the Placement Agent (the “Placement Agent Warrants” and, together with the Common Stock, the Warrants, and the Warrant Shares (as defined below) the “Securities”). The shares of Common Stock to be issued pursuant to the Warrants and the Placement Agent Warrants are collectively referred to herein as the “Warrant Shares.” The Securities are registered and to be issued pursuant to the Registration Statement on Form S-3 (File No. 333-228910), originally filed with the U.S. Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), on December 20, 2018 (the “Registration Statement”), and the related Prospectus (as defined below). The Registration Statement and the prospectus included therein, including the documents incorporated by reference therein, is referred to herein as the “Base Prospectus.” The final prospectus supplement, dated February 27, 2020, to be filed with the Commission pursuant to Rule 424(b)(5) under the Securities Act is referred to herein as the “Final Prospectus Supplement”. The Base Prospectus and the Final Prospectus Supplement are collectively referred to as the “Prospectus”.

In rendering this opinion, we have examined the Registration Statement, the Prospectus, and such other documents and reviewed such questions of law as we have deemed advisable in order to render our opinion set forth below. In such examination, we have assumed the genuineness of all signatures, the legal capacity of all natural persons, that all parties (other than the Company) had the requisite power and authority (corporate or otherwise) to execute, deliver and perform such agreements or instruments, that all such agreements or instruments have been duly authorized by all requisite action (corporate or otherwise), executed and delivered by such parties, that such agreements or instruments are valid, binding and enforceable obligations of such parties, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as certified, conformed or photostatic copies and the authenticity of the originals of such latter documents. In providing this opinion, we have further relied as to certain matters on information obtained from public officials and officers of the Company.

As a result of and subject to the foregoing, we are of the opinion that the Securities have been duly authorized for issuance, and upon the issuance and delivery of the Securities against payment of the consideration therefor, the Securities will be validly issued, fully paid and non-assessable.

Our opinion expressed above is limited to the General Corporation Laws of the State of Delaware and laws of the State of New York, in each case as currently in effect, and we express no opinion as to the effect on the matters covered by this letter of the laws of any other jurisdiction.

This opinion letter is expressly limited to the matters set forth above, and we render no opinion, whether by implication or otherwise, as to any other matters relating to the Company, the Securities, the Registration Statement or the Prospectus.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to being named under the caption “Legal Matters” contained in the Prospectus. In giving this consent, we do not hereby admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission promulgated thereunder.

Very truly yours,

/s/ Thompson Hine LLP

Thompson Hine LLP