EXHIBIT 23.1 CONSENT OF INDEPENDENT AUDITORS We consent to the incorporation by reference in the Registration Statement (Form S-8) pertaining to the 2002 SWAPIA Non-Qualified Stock Option Plan and the 2002 Mechanics Non-Qualified Stock Option Plan of Southwest Airlines Co. of our report dated January 16, 2002, 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, 2001, filed with the Securities and Exchange Commission. October 25, 2002