Exhibit 99.1


                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
AirlinesCo. (the "Company") for the period ended March 31, 2003 as filed with
the Securities and Exchange Commission on the date hereof (the "Report"), I,
Gary C. Kelly, Executive Vice President and Financial Officer of the Company,
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 22, 2003                        By /s/ Gary C. Kelly

                                             Gary C. Kelly
                                             Executive Vice President - Chief
                                             Financial Officer




















A signed original of this written statement required by Section 906 has been
provided to Southwest Airlines Co. and will be retained by Southwest Airlines
Co. and furnished to the Securities and Exchange Commission or its staff upon
request.



<Page>
                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, 2003 as filed
with the Securities and Exchange Commission on the date hereof (the
"Report"), I, James F. Parker, Chief Executive Officer of the Company,
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 22, 2003                        By /s/ James F. Parker

                                             James F. Parker
                                             Chief Executive Officer





















A signed original of this written statement required by Section 906 has been
provided to Southwest Airlines Co. and will be retained by Southwest Airlines
Co. and furnished to the Securities and Exchange Commission or its staff upon
request.