CERTIFICATION PURSUANT TO
                             18 U.S.C. SECTION 1350,
                             AS ADOPTED PURSUANT TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002


     In connection with the Quarterly  Report of Covenant  Transport,  Inc. (the
"Company")  on Form 10-Q for the period ended March 31, 2004,  as filed with the
Securities and Exchange  Commission on the date hereof (the  "Report"),  each of
the  undersigned  certifies,  pursuant  to 18 U.S.C.  Section  1350,  as adopted
pursuant to Section 906 of the  Sarbanes-Oxley  Act of 2002,  that,  to the best
knowledge of the undersigned:

     (1) The Report fully  complies  with the  requirements  of Section 13(a) or
15(d) of the Securities Exchange Act of 1934; and

     (2)  The  information  contained  in the  Report  fairly  presents,  in all
material  respects,  the  financial  condition  and results of operations of the
Company.

A signed  original of this  written  statement  required by Section 906 has been
provided to Covenant Transport, Inc. and will be retained by Covenant Transport,
Inc. and furnished to the Securities  and Exchange  Commission or its staff upon
request.


Date:    May 5, 2004              /s/ David R. Parker
                                 --------------------------
                                 David R. Parker
                                 Chief Executive Officer


                                  /s/ Joey B. Hogan
                                 --------------------------
                                 Joey B. Hogan
                                 Chief Financial Officer