WASHINGTON, D.C.  20549

                                   FORM 8-K

              Current Report Pursuant to Section 13 or 15(d) of
                    the Securities Exchange Act of 1934

        Date of Report (Date of earliest event reported): April 15, 2004

                            SOUTHWEST AIRLINES CO.
            (Exact name of registrant as specified in its charter)

               (State or other jurisdiction of incorporation)

            1-7259                                        74-1563240
    (Commission File Number)                 (IRS Employer Identification No.)

   P. O. Box 36611, Dallas, Texas                         75235-1611
 (Address of principal executive offices)                 (Zip Code)

      Registrant's telephone number, including area code (214) 792-4000

       (Former name or former address, if changed since last report)

Item 12.  Results of Operations and Financial Condition.

            On April 15, 2004, the Registrant issued a press release
announcing its financial results for the first quarter of 2004.  The press
release is furnished herewith as Exhibit 99.1 and is
incorporated herein by reference.
            The information furnished in this Item 12 shall not be deemed
"filed" for purposes of Section 18 of the Securities Exchange Act of 1934, as
amended, or otherwise subject to the liabilities of that section, nor shall
such information be deemed incorporated by reference in any filing under the
Securities Exchange Act of 1933, as amended, regardless of any general
incorporation language in such filing, except as shall be expressly set forth
by specific reference in such filing.

            Pursuant to the requirements of the Securities Exchange Act of
1934, the registrant has duly caused this report to be signed on its behalf by
the undersigned thereunto duly authorized.

                                            SOUTHWEST AIRLINES CO.

                                            By: /s/ Gary C. Kelly
                                                    Gary C. Kelly
                                                    Executive Vice President -
                                                    Chief Financial Officer

Date: April 15, 2004

                             INDEX TO EXHIBITS

         No.                               Exhibit
        99.1    Registrant's First Quarter 2004 Earnings Release.