Exhibit 5.1

October 21, 2022

Vaxart, Inc.

170 Harbor Way

Suite 300

South San Francisco, CA 94080

Ladies and Gentlemen:

Vaxart, Inc., a Delaware corporation (the “Company”), is filing with the U.S. Securities and Exchange Commission (the “Commission”) a Registration Statement on Form S-8 (the “Registration Statement”) for the registration, under the Securities Act of 1933, as amended (the “Securities Act”), of a total of 13,800,000 shares of common stock, $0.0001 par value, of the Company (the “Common Stock”), consisting of (1) 12,000,000 shares of Common Stock that are issuable at any time or from time to time under the Company’s 2019 Equity Incentive Plan (as amended to date, the “Incentive Plan”), and (2) 1,800,000 shares of Common Stock that are issuable at any time or from time to time under the Company’s 2022 Employee Stock Purchase Plan (the “ESPP”).

Item 601 of Regulation S-K and the instructions to Form S-8 require that an opinion of counsel concerning the legality of the securities to be registered be filed as an exhibit to a Form S-8 registration statement if the securities are original issue shares. This opinion is provided in satisfaction of that requirement as it relates to the Registration Statement.

In rendering this opinion, we have examined the Incentive Plan, ESPP, Registration Statement, the certificate of incorporation, as amended, and by-laws of the Company (each as amended and restated as of the date hereof) and such other records, instruments and documents as we have deemed advisable in order to render this opinion. In such examination, we have assumed the genuineness of all signatures, the legal capacity of all natural persons, the authenticity of all documents, certificates and instruments submitted to us as originals, the conformity to original documents of all documents, certificates and instruments submitted to us as certified, conformed or photostatic copies and the authenticity of the originals of such latter documents. Our opinion set forth below is based on the text of the Incentive Plan and the ESPP as referenced in the Exhibits Index to the Registration Statement and is limited to the General Corporation Laws of the State of Delaware 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.

As a result of the foregoing, and subject to the further limitations, qualifications and assumptions set forth herein, we are of the opinion that, under the laws of the State of Delaware, when issued pursuant to the Incentive Plan or the ESPP, the Common Stock that is the subject of the Registration Statement will be validly issued, fully paid and non-assessable.

In rendering this opinion, we have assumed that the resolutions authorizing the Company to issue the Common Stock pursuant to the Incentive Plan and the ESPP will be in full force and effect at all times at which the Common Stock is issued by the Company, and that the Company will take no action inconsistent with such resolutions. We have further assumed that each award under the Incentive Plan and the ESPP will be approved by the Board of Directors of the Company or an authorized committee of the Board of Directors.

This opinion letter speaks only as of the date hereof. We expressly disclaim any responsibility to advise you of any development or circumstance of any kind, including any change of law or fact that may occur after the date of this opinion letter that might affect the opinion expressed herein.

We hereby consent to the filing of this opinion letter as an exhibit to the Registration Statement. In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission.

Very truly yours,

/s/ Thompson Hine LLP

Thompson Hine LLP