Exhibit 5.1

[Letterhead of Thompson Hine LLP]

Vaxart, Inc.
385 Oyster Point Blvd., Suite 9A
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 offer and sale by the Company of up to $250,000,000 of shares (the “Shares”) of the Company’s common stock, par value $0.0001 per share, pursuant to that certain Open Market Sale Agreement^SM, dated as of October 13, 2020, by and among the Company, and Jefferies LLC and Piper Sandler & Co., as sales agents (the “Agreement”). The Shares will be offered and sold pursuant to the Company’s effective Registration Statement on Form S-3 (File No. 333-239751) (the “Registration Statement”) filed with the U.S. Securities and Exchange Commission (the “Commission”) on July 8, 2020 under the Securities Act of 1933, as amended (the “Securities Act”), relating to the sale of the Shares as set forth in a prospectus supplement, dated October 13, 2020 (the “Prospectus Supplement”), supplementing the prospectus dated July 8, 2020 (the “Base Prospectus” and together with the Prospectus Supplement, the “Prospectus”). This opinion letter is furnished to you at your request to enable you to fulfill the requirements of Item 601(b)(5) of Regulation S-K in connection with the Registration Statement.

In our capacity as such counsel, we have examined originals or copies of those corporate and other records, documents and agreements we considered appropriate, including the Company’s certificate of incorporation and bylaws, Agreement, the Registration Statement and the Prospectus. As to relevant factual matters, we have relied upon, among other things, factual representations we have received from the Company. In addition, we have obtained and relied upon those certificates of public officials we considered appropriate.

We have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals and the conformity with originals of all documents submitted to us as copies.

On the basis of such examination, our reliance upon the assumptions in this opinion and our consideration of those questions of law we considered relevant, and subject to the limitations and qualifications in this opinion, we are of the opinion that the Shares, when issued and sold in accordance with the Registration Statement and the Prospectus, will by validly issued, fully paid and non-assessable.

The law covered by this opinion is limited to the present Delaware General Corporation Law and the present federal law of the United States. We express no opinion as to the laws of any other jurisdiction and no opinion regarding the statutes, administrative decisions, rules, regulations or requirements of any county, municipality, subdivision or local authority of any jurisdiction.