1

                                                                    Exhibit 23.1


                         CONSENT OF INDEPENDENT AUDITORS

We consent to the incorporation by reference in the Registration Statement (Form
S-8) pertaining to the Southwest Airlines Co. Excess Benefit Plan of our report
dated January 23, 1998 with respect to the consolidated financial statements of
Southwest Airlines Co. included in its Annual Report (Form 10-K) for the year
ended December 31, 1997 filed with the Securities and Exchange Commission.


                                                           /s/ Ernst & Young LLP

                                                               ERNST & YOUNG LLP


Dallas, Texas
November 19, 1998