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 May 2004

                           A/S STEAMSHIP COMPANY TORM
                 (Translation of registrant's name into English)

                                   Marina Park
                                Sundkrogsgade 10
                              DK-2100 Copenhagen 0
                                     Denmark
                    (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

     Set forth herein as Exhibit 1 is a copy of a "Prospectus: Increase of the
Share Capital - Issue of Bonus Shares" issued by A/S STEAMSHIP COMPANY TORM to
The Copenhagen Stock Exchange on April 27, 2004.


Exhibit I - Prospectus: Increase of the Share Capital - Issue of Bonus Shares




     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.

                                          A/S STEAMSHIP COMPANY TORM
                                                  (registrant)



Dated: May 12, 2004                       By: /s/ Klaus Nyborg
                                          --------------------------
                                              Klaus Nyborg
                                              Chief Financial Officer

03810.0001 #484108