Exhibit 5.1

Southwest Airlines Co.

Mark R. Shaw

Executive Vice President & Chief Legal &

Regulatory Officer & Corporate Secretary

2702 Love Field Drive

Dallas, TX 75235

(214) 792-6143

May 31, 2024

Southwest Airlines Co.

2702 Love Field Drive

P.O. Box 36611

Dallas, TX 75235-1611

Ladies and Gentlemen:

I am the Executive Vice President & Chief Legal & Regulatory Officer & Corporate Secretary of Southwest Airlines Co., a Texas corporation (the “Company”). This opinion is being delivered in connection with the registration under the Securities Act of 1933, as amended (the “Securities Act”), of 4,750,000 shares (the “Shares”) of the Company’s common stock, par value $1.00 per share, pursuant to the Company’s registration statement on Form S-8 (the “Registration Statement”) filed with the Securities and Exchange Commission on May 31, 2024, which Shares are to be issued pursuant to the Southwest Airlines Co. Amended and Restated 2007 Equity Incentive Plan (the “Plan”).

In rendering the opinions set forth below, I have reviewed and relied upon the original or certified copies of such documents, corporate or other records, certificates, and other papers as I have deemed necessary for the purpose of rendering such opinions. In making the foregoing examinations, I have assumed the genuineness of all signatures on original documents, the authenticity of all documents submitted to me as originals, and the conformity to original documents of all copies submitted to me.

Based upon the foregoing, subject to comments hereinafter stated, and limited in all respects to the laws of the State of Texas and the federal laws of the United States of America, in each case as in effect on the date hereof, it is my opinion that the Shares, when issued by the Company pursuant to the terms and conditions of the Plan, will be validly issued, fully paid, and nonassessable.

I consent to the use of this opinion as an exhibit to the Registration Statement and the reference to me in Item 5 of the Registration Statement. In giving this consent, I do not thereby admit that I am within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations thereunder.

Sincerely,

/s/ Mark R. Shaw

Mark R. Shaw