# FORM 6-K
SECURITIES AND EXCHANGE COMMISSION Washington, D.C. 20549

# Report of Foreign Private Issuer

# Pursuant to Rule 13a-16
or 15d-16of the Securities Exchange Act of 1934

For the month
  of June, 2004Commission File Number 1-11080

THE ICA CORPORATION
HOLDING COMPANY(Translation of registrants name into English)

Minería No. #14511800 México D.F.
(Address of principal executive offices)

Form 20-F....X.....Form 40-F.........

Indicate by check mark if the
registrant is submitting the Form 6-K in paper as permitted by Regulation S-T Rule
101(b)(1): ____ 

Indicate by check mark if the registrant is submitting the Form 6-K in
paper as permitted by Regulation S-T Rule 101(b)(7): ____ 

Indicate by check mark whether by furnishing the information contained in this Form, the registrant 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...

If Yes is marked, indicate
below the file number assigned to the registrant in connection with Rule 12g3-2(b): 82-
________

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| | PRESS
        RELEASE
| | ---------------------
|

|For more information
        contact:
      Ing. Alonso Quintana(5255) 5272-9991 x3468alonso.quintana@ica.com.mx
      Lic. Paloma
        Grediaga(5255) 5272-9991 x3470paloma.grediaga@ica.com.mx | in the United States:
        Zemi Communications
      Daniel Wilson
        (212) 689-9560d.b.m.wilson@zemi.com
|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | -----------------------------------------------------------------------------------------------------------------



ICA
  SIGNS A JOINT VENTURE AGREEMENT FOR THE CONSTRUCTION OF A PS. 195 MILLION PROJECT

Mexico
  City, June 7, 2004 Empresas ICA Sociedad Controladora (NYSE and BMV: ICA),the largest engineering, procurement, and construction company in Mexico, today
  announced the signing of a 50-50 joint venture agreement between its subsidiary,
  Ingenieros Civiles Asociados, S.A. de C.V., and Construcciones y Trituraciones
  S.A. de C.V. (Cotrisa), for the joint development of a project, valued at Ps.
  195 million at the time of the contract award, which is part of the sanitation
  and drainage enlargement works in Mexico City.

On December 22, 2003, Cotrisa
  was awarded the contract for the development of the Rio de los Remedios Interceptor
  Tunnel by Fideicomiso 1928, coordinated by the National Water Commission. This
  work consists in the construction of five shaftways, the excavation of 9,874.6
  meters of tunnel, and the fabrication of 9,600 concrete sewer sections. This
  contract is part of the waste water management project in the Valley of Mexico.

Combining efforts and seeking
  synergies, ICA and Cotrisa will jointly fabricate the 9,600 sections overa term of 18 months, with work beginning on June 1 and scheduled completion
  on November 30, 2005. This portion of the project has a total value of Ps. 195
  million, at the date of the contract award.

Founded in 1947, ICA
  has completed construction and engineering projects in 21 countries. ICAs
  principal business units include Civil Construction, and Industrial Construction.
  Through its subsidiaries, ICA also develops housing, manages airports, and operates
  tunnels, highways, and municipal services under government concession contracts
  and/or partial sale of long term contract rights.



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   #

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SIGNATURE

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.

Date: June 7,
  2004

| | Empresas ICA Sociedad Controladora,
S.A. de C.V.                                  
| | ----------------------------------------------------------------------------------
| |                                                                                   
| | /s/ JOSE LUIS GUERRERO
Name: Dr. José Luis Guerrero
Title: Vice President, Finance