Exhibit 5.1

November 19, 2010

Southwest Airlines Co.

2702 Love Field Drive

Dallas, Texas 75235

Ladies and Gentlemen:

We are acting as counsel for Southwest Airlines Co., a Texas corporation (“Southwest”), in connection with the proposed issuance by Southwest of up to 57,931,897 shares (the “Shares”) of common stock, par value $1.00 per share, of Southwest. The Shares are proposed to be offered to holders of the common stock, par value $0.001 per share, of AirTran Holdings, Inc., a Nevada corporation (“AirTran”), in connection with the merger of Guadalupe Holdings Corp., a Nevada corporation and wholly owned subsidiary of Southwest (“Merger Sub”), with and into AirTran, with AirTran surviving the merger as a wholly owned subsidiary of Southwest, pursuant to an Agreement and Plan of Merger dated as of September 26, 2010 (the “Merger Agreement”), among Southwest, AirTran and Merger Sub. This opinion is being delivered in connection with Southwest’s Registration Statement on Form S-4 (the “Registration Statement”) relating to the registration under the Securities Act of 1933 of the offering and sale of the Shares pursuant to the Merger Agreement.

We are rendering the opinion hereinafter set forth as of the time the Registration Statement becomes effective in accordance with Section 8(a) of the Securities Act of 1933.

In connection with the opinion hereinafter set forth, we have assumed that the Registration Statement will have become effective and the Shares will be issued and sold in compliance with applicable federal and state securities laws and in the manner described in the Registration Statement and the proxy statement/prospectus therein.

In rendering the opinion set forth below, we have reviewed such certificates, documents and records as we have deemed relevant for the purposes of rendering such opinion. As to any facts material to our opinion, we have made no independent investigation or verification of such facts and have relied, to the extent that we deem such reliance proper, upon certificates of public officials and officers or other representatives of Southwest.

In rendering the opinion expressed below, we have assumed (a) the legal capacity of all natural persons, (b) the genuineness of all signatures, (c) the authority of all persons signing all documents submitted to us on behalf of the parties to such documents, (d) the

			November 19, 2010  Page  2

authenticity of all documents submitted to us as originals, (e) the conformity to authentic original documents of all documents submitted to us as copies, and (f) that all information contained in all documents reviewed by us is true, correct and complete. In addition, we have assumed that (a) the Shares will be issued in accordance with the terms of the Merger Agreement, (b) the full consideration for each Share will be received by Southwest and will not be less than par value for each Share, and (c) certificates evidencing the Shares will be properly executed and delivered by Southwest in accordance with the Texas Business Organizations Code (the “TBOC”).

Based upon the foregoing, and subject to the assumptions, qualifications, exceptions and limitations set forth herein, it is our opinion that the Shares, when issued by Southwest in accordance with the Merger Agreement, will be validly issued, fully paid and nonassessable.

The foregoing opinion is limited to matters involving the federal laws of the United States of America and the TBOC, and we do not express any opinion as to the laws of any other state or jurisdiction.

The opinion expressed herein is rendered only to you in connection with the Registration Statement. The opinion expressed herein may not be relied upon by you for any other purpose, or furnished to, quoted to or relied upon by any other person, firm or corporation or for any other purpose.

We hereby consent to the filing of this opinion letter as an exhibit to the Registration Statement and the references to us under the heading “Legal Matters” in the proxy statement/prospectus that forms 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 of 1933 and the rules and regulations of the Securities and Exchange Commission promulgated thereunder.

We express no opinion as to any matter other than as expressly set forth above, and no opinion on any other matter may be inferred or implied herefrom. We undertake no, and hereby expressly disclaim any, obligation to advise Southwest or anyone else of any change in any matter set forth herein.

Very truly yours,

/s/ Vinson & Elkins L.L.P.