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 2006

                           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 Announcement No. 3 - 2006 issued
by A/S STEAMSHIP COMPANY TORM to The Copenhagen Stock Exchange on
April 4, 2006.



Exhibit 1
---------

ANNOUNCEMENT NO. 3 - 2006

                                                        4 April 2006


Following Dampskibsselskabet NORDEN's publication of its annual report for 2005,
TORM would hereby as the company's biggest shareholder like to express its
satisfaction with the result achieved and with the expectations for 2006.

Against this background, TORM will in the coming period actively assess its
shareholding in NORDEN.


Contact

A/S Dampskibsselskabet TORM      Telephone +45 39 17 92 00
Tuborg Havnevej 18               Klaus Kjaerulff, CEO
DK-2900 Hellerup - Denmark       Klaus Nyborg, CFO


About TORM

TORM is one of the World's leading carriers of refined oil products and has
significant activities in the bulk market. The Company operates close to 100
modern and secure vessels, most of them in pool co-operation with other
respected shipping companies, sharing TORM's commitment to safety, environmental
responsibility and customer service.

TORM was founded in 1889 and has constantly adapted itself and benefited from
the significant changes characterizing shipping. The Company conducts business
all over the World and is headquartered in Copenhagen, Denmark. TORM's shares
are listed in Copenhagen (ticker TORM) as well as on NASDAQ (ticker TRMD). For
more information, visit www.torm.com.


SAFE HARBOUR STATEMENT - FORWARD LOOKING STATEMENTS
-------------------------------------------------------------------------------
Matters discussed in this release may constitute forward-looking statements.
Forward-looking statements reflect our current views with respect to future
events and financial performance and may include statements concerning plans,
objectives, goals, strategies, future events or performance, and underlying
assumptions and other statements, which are other than statements of historical
facts.

The forward-looking statements in this release are based upon various
assumptions, many of which are based, in turn, upon further assumptions,
including without limitation, management's examination of historical operating
trends, data contained in our records and other data available from third
parties. Although TORM believes that these assumptions were reasonable when
made, because these assumptions are inherently subject to significant
uncertainties and contingencies which are difficult or impossible to predict and
are beyond our control, TORM cannot assure you that it will achieve or
accomplish these expectations, beliefs or projections.

Important factors that, in our view, could cause actual results to differ
materially from those discussed in the forward-looking statements include the
strength of world economies and currencies, changes in charter hire rates and
vessel values, changes in demand for "tonne miles" of crude oil carried by oil
tankers, the effect of changes in OPEC's petroleum production levels and
worldwide oil consumption and storage, changes in demand that may affect
attitudes of time charterers to scheduled and unscheduled drydocking, changes in
TORM's operating expenses, including bunker prices, dry-docking and insurance
costs, changes in governmental rules and regulations including requirements for
double hull tankers or actions taken by regulatory authorities, potential
liability from pending or future litigation, domestic and international
political conditions, potential disruption of shipping routes due to accidents
and political events or acts by terrorists.

Risks and uncertainties are further described in reports filed by TORM with the
US Securities and Exchange Commission, including the TORM Annual Report on Form
20-F and its reports on Form 6-K.
-------------------------------------------------------------------------------



                                   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 7, 2006
                                                 By: /s/ Klaus Nyborg
                                                     --------------------------
                                                     Klaus Nyborg
                                                     Chief Financial Officer


SK 03810 0001 659706