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 2005

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

                               Tuborg Havnevej 18
                                DK-2900 Hellerup
                                     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 Share Statement No. 3
- 2005 issued by A/S STEAMSHIP COMPANY TORM to The Copenhagen Stock Exchange on
March 31, 2005.



Exhibit 1

SHARE STATEMENT No. 3 - 2005


31 March 2005



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


-------------------------------------------------------------------------------
Securities     Trade date  Holding     Market   Total Holding     Total market
  Code                     number      value      number            value
-------------------------------------------------------------------------------
DK0010281468   29.03.2005  +8,140    2,354,820   2,347,043      704,042,240.00
-------------------------------------------------------------------------------


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 14, 2005
                                                   By: /s/ Klaus Nyborg
                                                   --------------------------
                                                   Klaus Nyborg
                                                   Chief Financial Officer

03810.0001 #563306