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. 2000 Flight Simulator Technicians Non-Qualified Stock Option Plan of our report dated January 18, 2000 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, 1999, filed with the Securities and Exchange Commission. /s/ ERNST & YOUNG LLP ERNST & YOUNG LLP January 12, 2001