<DOCUMENT>
<TYPE>EX-13.CERTIFICATION
<SEQUENCE>6
<FILENAME>d583542_13-1.txt
<DESCRIPTION>EX-13.1
<TEXT>
                                                                   Exhibit 13.1

                      CHIEF EXECUTIVE OFFICER CERTIFICATION
                       PURSUANT TO 18 U.S.C. SECTION 1350

          In  connection  with this  Annual  Report of  Nordic  American  Tanker
Shipping  Limited (the  "Company") on Form 20-F for the year ended  December 31,
2004 as filed with the  Securities  and  Exchange  Commission  (the "SEC") on or
about the date hereof (the  "Report"),  I,  Herbjorn  Hansson,  Chief  Executive
Officer of the Company,  certify, pursuant to 18 U.S.C. Section 1350, as adopted
pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

     (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 has been provided to the
Company and will be retained  by the  Company  and  furnished  to the SEC or its
staff upon request.

Date: June 30, 2005

/s/ Herbjorn Hansson
---------------------------------
Chief Executive Officer


<PAGE>


</TEXT>
</DOCUMENT>
