Exhibit 31.1


                                  CERTIFICATION

      I, Gary C. Kelly, Chief Executive Officer and Vice Chairman of the
Board of Directors of Southwest Airlines Co., certify that:

      1.      I have reviewed this quarterly report on Form 10-Q for the
quarter ended March 31, 2005 of Southwest Airlines Co.;

      2.      Based on my knowledge, this report does not contain any untrue
statement of a material fact or omit to state a material fact necessary to
make the statements made, in light of the circumstances under which such
statements were made, not misleading with respect to the period covered by
this report;

      3.      Based on my knowledge, the financial statements, and other
financial information included in this report, fairly present in all material
respects the financial condition, results of operations and cash flows of the
registrant as of, and for, the periods presented in this report;

      4.      The registrant's other certifying officer(s) and I are
responsible for establishing and maintaining disclosure controls and
procedures (as defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) and
internal control over financial reporting (as defined in Exchange Act Rules
13a-15(f) and 15d-15(f)) for the registrant and have:

      (a)     designed such disclosure controls and procedures, or caused
such disclosure controls and procedures to be designed under our supervision,
to ensure that material information relating to the registrant, including its
consolidated subsidiaries, is made known to us by others within those
entities, particularly during the period in which this report is being
prepared;

      (b)     designed such internal control over financial reporting, or
caused such internal control over financial reporting to be designed under
our supervision, to provide reasonable assurance regarding the reliability of
financial reporting and the preparation of financial statements for external
purposes in accordance with generally accepted accounting principles;

      (c)     evaluated the effectiveness of the registrant's disclosure
controls and procedures and presented in this report our conclusions about
the effectiveness of the disclosure controls and procedures, as of the end of
the period covered by this report based on such evaluation; and

      (d)     disclosed in this report any change in the registrant's
internal control over financial reporting that occurred during the
registrant's most recent fiscal quarter (the registrant's fourth fiscal
quarter in the case of an annual report) that has materially affected, or is
reasonably likely to materially affect, the registrant's internal control over
financial reporting; and

      5.     The registrant's other certifying officer(s) and I have
disclosed, based on our most recent evaluation of internal control over

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financial reporting, to the registrant's auditors and the audit committee of
the registrant's board of directors (or persons performing the equivalent

functions):

      (a)    all significant deficiencies and material weaknesses in the
design or operation of internal control over financial reporting which are
reasonably likely to adversely affect the registrant's ability to record,
process, summarize and report financial information; and

      (b)    any fraud, whether or not material, that involves management or
other employees who have a significant role in the registrant's internal
control over financial reporting.


Date: April 15, 2005
                                       By:   /s/ Gary C. Kelly
                                             Gary C. Kelly
                                             Chief Executive Officer and
                                             Vice Chairman of the Board
                                             of Directors