FORM 6-K


                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D. C. 20549



                        Report of Foreign Private Issuer
                      Pursuant to Rule 13a-16 or 15d-16 of
                       the Securities Exchange Act of 1934

                           For the month of March 2005


                     NORDIC AMERICAN TANKER SHIPPING LIMITED
                 (Translation of registrant's name into English)

                                  Canon's Court
                               22 Victoria Street
                                 Hamilton HM 12
                                     Bermuda
                    (Address of principal executive offices)

          Indicate by check mark whether the registrant files or will file
annual reports under cover Form 20-F or Form 40-F.

                        Form 20-F  [X]   Form 40-F [_] 

          Indicate by check mark whether the registrant by furnishing the
information contained in this Form is also thereby furnishing the information to
the commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of
1934.

                              Yes  [_]     No [X] 





INFORMATION CONTAINED IN THIS FORM 6-K REPORT

          Attached hereto as Exhibit 99.1 is a copy the Undereritng Agreement
dated March 2, 2005, between Nordic American Tanker Shipping Limited (the
"Company") and Bear, Stearns & Co. Inc., UBS Securities LLC and DNB Nor Markets,
Inc. Information furnished on this Report of Foreign Private Issuer on Form 6-K
shall be deemed to be incorporated by reference as Exhibit 1.1 in the Company's
Registration Statement on Form F-3 (File No. 333-118128).





                                   SIGNATURES


          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.


                                         NORDIC AMERICAN TANKER SHIPPING LIMITED
                                         ---------------------------------------
                                                        (registrant)



Dated:  March 4, 2005                     By: /s/ Herbjorn Hansson
                                              --------------------
                                                  Herbjorn Hansson
                                                  President and
                                                  Chief Executive Officer




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