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 November 2004
                     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 the  execution  copy of the  
Underwriting Agreement  dated November 17, 2004, among 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:  November 19, 2004                          By: /s/ Herbjorn Hansson
                                                       -------------------------
                                                       Herbjorn Hansson
                                                       President and
                                                       Chief Executive Officer