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 October 2004

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

                               Tuborg Havnevej 18
                                DK-2900 Hellerup
                    (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|


          Set forth herein as Exhibit 1 is a copy of Announcement No. 12 - 2004
- TORM increases expectations to 2004 profit before tax and value adjustment to
DKK 1,100-1,150 mill. issued by A/S STEAMSHIP COMPANY TORM to The Copenhagen
Stock Exchange on October 5, 2004.

Exhibit 1


5 October 2004

TORM increases expectations to 2004 profit before tax and value adjustment to
DKK 1,100-1,150 mill.

o    In the third quarter and into the fourth quarter of 2004 TORM's Tanker
     division has achieved higher freight rates and therefore higher earnings
     than TORM's expectations, as announced 12 August 2004. This is primarily
     due to continued strong global demand for refined products. In the Bulk
     division, rates have developed according to expectations.

o    TORM increases its expectations for 2004 profit before tax and value
     adjustment on Norden shares from DKK 875-925 mill. as announced 12 August
     2004, to DKK 1,100-1,150 mill.

o    The increase in expectations - in total DKK 225 mill. - consists of
     improved earnings of approximately DKK 100 mill. and extraordinary dividend
     payment from Norden, corresponding to a DKK 127 mill. income for TORM.

o    The expected result consists of earnings from TORM's own operations of DKK
     900-950 mill. and a total DKK 200 mill. dividend payment received from
     Norden in 2004.

o    As of 4 October 2004, the unrealised gain in 2004 on TORM's investment in
     Norden was DKK 846 mill., based on a share price of DKK 2,467/share.

o    The report for the first nine months of 2004 is expected to be released on
     11 November 2004 as previously announced.

A/S Dampskibsselskabet TORM
Contact persons: Klaus Kjaerulff, CEO, tel. +45 3917 9200
                 Klaus Nyborg, CFO, tel. +45 3917 9200

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

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 dry-docking, 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.


          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

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

03810.0001 #517095