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 April 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 Share Statement No. 8 -
2004 issued by A/S STEAMSHIP COMPANY TORM to The Copenhagen Stock Exchange on
April 14, 2004


Exhibit 1
---------

SHARE STATEMENT No.  8 - 2004

14 April 2004

Please below find the total shareholdings of all insiders and related parties,
including the shareholding of the entire Board of Directors (including related
parties) and the entire Executive Board of Directors (including related parties)
pursuant to the Danish Securities Trading Act.

--------------------------------------------------------------------------------
      Securities code                    Holding                 Market value
       DK0010281468                      (number)                   (DKK)

                                    As at 7 April 2004        As at 7 April 2004
--------------------------------------------------------------------------------
Board of Directors                               9,049              3,103,626.02
(incl. related parties)
--------------------------------------------------------------------------------
Executive Board of Directors                    15,483              5,310,359.34
(incl. related parties)
--------------------------------------------------------------------------------
All (incl. related parties)                  1,194,192            409,583,972.16
--------------------------------------------------------------------------------

A/S Dampskibsselskabet TORM
Contact person: Klaus Nyborg, CFO (tel.: +45 39 17 92 00)


                                   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: April 16, 2004                      By: /s/ Klaus Nyborg
                                               ----------------
                                               Klaus Nyborg
                                               Chief Financial Officer

03810.0001 #479349