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 May 2004

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

                                   Marina Park
                                Sundkrogsgade 10
                              DK-2100 Copenhagen 0
                    (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 a Announcement No. 8 - 2004
issued by A/S STEAMSHIP COMPANY TORM to The Copenhagen Stock Exchange on April
26, 2004.

Exhibit 1


26 April 2004

Prospectus Notice

Occasioned by the resolution by the shareholders of A/S Dampskibsselskabet TORM
(hereinafter "TORM") at the Annual General Meeting in the Company held on 20
April 2004 to increase the share capital from nominally DKK 182,000,000 by
nominally DKK 182,000,000 to nominally DKK 364,000,000 through the issue of
18,200,000 bonus shares of DKK 10 each, TORM will on 27 April 2004 publish a
prospectus. Publication will be made through the Copenhagen Stock Exchange and
the prospectus will, in addition to being forwarded to all the Company's
registered shareholders, be made available for review at TORM's main office at
the address Marina Park, Sundkrogsgade 10, 2100 Copenhagen from where a copy can
be received upon request.

The Company's existing shareholders will receive bonus shares at the ratio of
1:1 and such that one share of DKK 10 entitles the holder to one new share of
DKK 10.

Shareholders of TORM whose shares as of the daily update on Thursday 6 May 2004
are registered with the Danish Securities Centre (in Danish:
"Vaerdipapircentralen") will be entitled to receive bonus shares. The bonus
shares will be allotted on 6 May 2004 by registration on the shareholder's
account with the Danish Securities Centre. The value date of the registration
will be 10 May 2004. The shareholders will receive a separate notification of
the registration from the Danish Securities Centre.

As for the rights of holders of ADR certificates to receive bonus shares,
reference is made to the provisions thereon in the prospectus.

The new shares will be admitted for listing on the Copenhagen Stock Exchange on
4 May 2004.

Yours sincerely,

A/S Dampskibsselskabet TORM

N.E. Nielsen
Chairman of the Board of Directors

Contact Person:   Klaus Nyborg, CFO, tel.: +45 39 17 92 00

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 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.


            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: May 6, 2004                       By: /s/ Klaus Nyborg
                                                 Klaus Nyborg
                                                 Chief Financial Officer

03810.0001 #484088