Solaris Energy Infrastructure (SEI) 8-K Solaris Energy Infrastructure, Inc. Announces Pricing of Underwritten Public Offering of Class A Common Stock

Exhibit 5.1

December 11, 2024

Solaris Energy Infrastructure, Inc.

9651 Katy Freeway, Suite 300

Houston, Texas 77024

Ladies and Gentlemen:

We have acted as counsel for Solaris Energy Infrastructure, Inc., a Delaware corporation (the “Company”), with respect to certain legal matters in connection with (a) the proposed issuance and sale by the Company of up to 6,500,000 shares (the “Primary Shares”) of Class A common stock, par value $0.01 (the “Class A Common Stock”) and (b) the proposed sale by Yorktown Energy Partners X, L.P. (the “Selling Stockholder”) of up to 975,000 shares (the “Secondary Shares,” and together with the Primary Shares, the “Shares”) of Class A Common Stock (the “Redemption Common Stock”). The Shares are being offered, issued and sold pursuant to an Underwriting Agreement dated December 10, 2024 by and among the Company, the Selling Stockholder and Santander US Capital Markets LLC, as representative of the several underwriters named on Schedule B thereto (the “Underwriting Agreement”).

We have participated in the preparation of a Prospectus Supplement dated December 10, 2024 (the “Prospectus Supplement”), forming part of a Registration Statement on Form S-3 filed with the Securities and Exchange Commission (the “SEC”) on November 18, 2024, and declared effective by the SEC (File No. 333- 283308) on November 25, 2024 (the “Registration Statement”), which also contains two base prospectuses (the “Base Prospectuses” and, together with the Prospectus Supplement, the “Prospectus”). The Prospectus Supplement has been filed pursuant to Rule 424(b) promulgated under the Securities Act of 1933, as amended (the “Securities Act”).

In rendering the opinions set forth below, we have examined and relied upon (i) the Registration Statement and the Prospectus; (ii) the Amended and Restated Certificate of Incorporation of the Company, as amended; (iii) the Amended and Restated Bylaws of the Company, as amended; (iv) the Second Amended and Restated Limited Liability Company Agreement of Solaris Energy Infrastructure, LLC, as amended (“Solaris LLCA”); (v) the Underwriting Agreement; (vi) resolutions of the Board of Directors of the Company and of the Pricing Committee relating to the offering of the Shares; and (vii) such other certificates and other instruments and documents as we consider appropriate for purposes of the opinions hereafter expressed.

In connection with this opinion, we have assumed that all Shares will be issued and sold in the manner stated in the Prospectus and the Underwriting Agreement.

Based upon the foregoing and subject to the assumptions, exceptions, limitations and qualifications set forth herein, we are of the opinion that:

1. The Primary Shares, when issued and delivered against payment therefor in accordance with the Underwriting Agreement, will be validly issued, fully paid and non-assessable.

2. The Secondary Shares, when certificates representing the shares of the Redemption Common Stock have been duly executed, countersigned, registered, and delivered (or non-certificated shares of Redemption Common Stock shall have been properly issued) in accordance with the Solaris LLCA, then the shares of Redemption Common Stock will be legally issued, fully paid, and non-assessable.

Vinson & Elkins LLP Attorneys at Law Austin Dallas Denver Dubai Dublin Houston London Los Angeles New York Richmond San Francisco Tokyo Washington 845 Texas Avenue, Suite 4700 Houston, TX 77002 Tel +1.713.758.2222 Fax +1.713.758.2346 velaw.com

December 11, 2024 Page 2

The opinions expressed herein are qualified in the following respects:

A. We have assumed that (i) each document submitted to us for review is accurate and complete, each such document that is an original is authentic, each such document that is a copy conforms to an authentic original and all signatures on each such document are genuine, and (ii) each certificate from governmental officials reviewed by us is accurate, complete and authentic, and all official public records are accurate and complete.

B. This opinion is limited in all respects to the federal laws of the United States, the Delaware General Corporation Law and the Constitution of the State of Delaware, as interpreted by the courts of the State of Delaware and of the United States. We are expressing no opinion as to the effect of the laws of any other jurisdiction.

We hereby consent to the filing of this opinion as Exhibit 5.1 to the Company’s Current Report on Form 8-K dated on or about the date hereof, to the incorporation by reference of this opinion into the Registration Statement and to the reference to our firm under the caption “Legal Matters” in the Prospectus forming a part of the Registration Statement. 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.

Very truly yours,

/s/ Vinson & Elkins L.L.P.

Vinson & Elkins LLP Attorneys at Law Austin Dallas Denver Dubai Dublin Houston London Los Angeles New York Richmond San Francisco Tokyo Washington 845 Texas Avenue, Suite 4700 Houston, TX 77002 Tel +1.713.758.2222 Fax +1.713.758.2346 velaw.com