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 June 30, 2005 as filed with
the Securities and Exchange Commission on the date hereof (the "Report"),
Gary C. Kelly, Chief Executive Officer and Vice Chairman of the Board of
Directors 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:  July 15, 2005
                                          By   /s/ Gary C. Kelly
                                               Gary C. Kelly
                                               Chief Executive Officer and
                                               Vice Chairman of the Board
                                               of Directors


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