Exhibit 32.1

CERTIFICATION PURSUANT TO 18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report on Form 10-Q of Southwest Airlines Co. (the “Company”) for the period ended March 31, 2012 as filed with the Securities and Exchange Commission (the “Report”), Gary C. Kelly, Chief Executive Officer of the Company, and Laura H. Wright, Chief Financial Officer of the Company, each certify pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

(1)           The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

(2)           The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date:  April 25, 2012

By:	/s/ Gary C. Kelly
	Gary C. Kelly
	Chief Executive Officer

By:	/s/ Laura H. Wright
	Laura H. Wright
	Chief Financial Officer