UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549


                                    FORM 6-K

                        Report of Foreign Private Issuer

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

                           -------------------------

                          Date of report: July 1, 2004

                           TEEKAY SHIPPING CORPORATION
             (Exact name of Registrant as specified in its charter)

                                    TK House
                             Bayside Executive Park
                          West Bay Street & Blake Road
                       P.O. Box AP-59212, Nassau, Bahamas
                     (Address of principal executive office)


                           -------------------------

     [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 if the  registrant  is  submitting  the Form 6-K in
paper as permitted by Regulation S-T Rule 101(b)(1):       ]
                                                    -------

                        Yes                  No        X
                              ---------           ----------

     [Indicate by check mark if the  registrant  is  submitting  the Form 6-K in
paper as permitted by Regulation S-T Rule 101(b)(7):       ]
                                                    -------

                        Yes                  No        X
                              ---------           ----------

     [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
                              ---------           ----------


     [If  "Yes" is  marked,  indicate  below  the file  number  assigned  to the
registrant in connection with Rule 12g3-2(b):82-       ]
                                                -------




Item 1 - Information Contained in this Form 6-K Report

     Attached  as  Exhibit I is a copy of an  announcement  of  Teekay  Shipping
Corporation (the "Company"), dated July 1, 2004.


     THIS  REPORT  ON FORM 6-K IS  HEREBY  INCORPORATED  BY  REFERENCE  INTO THE
FOLLOWING REGISTRATION STATEMENTS OF THE COMPANY.

     --   REGISTRATION  STATEMENT ON FORM F-3 (NO.  33-97746) FILED WITH THE SEC
          ON OCTOBER 4, 1995;
     --   REGISTRATION  STATEMENT ON FORM S-8 (NO. 333-42434) FILED WITH THE SEC
          ON JULY 28, 2000; AND
     --   REGISTRATION STATEMENT ON FORM F-3 (NO. 333-102594) FILED WITH THE SEC
          ON JANUARY 17, 2003.






                                   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.

                                    TEEKAY SHIPPING CORPORATION


Date: July 1, 2004         By:      /s/ Peter Evensen
                                    ------------------------------------
                                    Peter Evensen
                                    Executive Vice President and Chief
                                    Financial Officer
                                    (Principal Financial and Accounting Officer)