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. 7 - 2004
issued by A/S STEAMSHIP  COMPANY TORM to The Copenhagen  Stock Exchange on April
7, 2004





Exhibit 1


SHARE STATEMENT No. 7 - 2004



7 April 2004


This is to notify you of changes in the shareholdings of the company's  insiders
pursuant according to the Danish Securities Trading Act.




Securities     Trade        Holding   Market       Total Holding   Total market
code           date         number    value           number          value
----           ----         ------    -----           ------          -----

DK0010281468   05.04.2004   -4,000    1,400,000.00  1,194,198     414,899,968.00
DK0010281468   06.04.2004   -3,530    1,238,023.40  1,194,198     414,899,968.00



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 12, 2004                                 By: /s/ Klaus Nyborg
                                                      -----------------------
                                                          Klaus Nyborg
                                                       Chief Financial Officer
03810.0001 #477915