Washington, D.C. 20549

                              FORM 8-K
                           CURRENT REPORT

               PURSUANT TO SECTION 13 OR 15(d) OF THE
                  SECURITIES EXCHANGE ACT OF 1934

          DATE OF REPORT (date of earliest event reported)

                           JUNE 21, 1994

                        Halliburton Company
       (Exact name of registrant as specified in its charter)

State or other                Commission          IRS Employer
jurisdiction                  File Number         Identification
of incorporation                                  Number

Delaware                      1-3492              No. 73-0271280

                         3600 Lincoln Plaza
                       500 North Akard Street
                      Dallas, Texas 75201-3391
              (Address of principal executive offices)

                  Registrant's telephone  number,
                 including area code - 214/978-2600

                         Page 1 of 6 pages
                The Exhibit Index appears on Page 4
Item 5.   Other Events

     The registrant may, at its option, report under this item any events, with
respect to which information is not otherwise called for by this form, that the
registrant deems of importance to security holders.

     On June 21, 1994, the registrant issued a press release entitled Shell
Launches Massive Coiled-Tubing Drilling Program -- Halliburton Drilling 68
Wells -- pertaining, among other things, to a coiled-tubing drilling program
with Halliburton Energy Services for injection wells in a California field.

     The foregoing summary is subject to the full text of the press release with
respect thereto, a copy of which is attached hereto as Exhibit 20, which exhibit
is incorporated herein by reference.

Item 7.   Financial Statements and Exhibits

     List below the financial statements, pro forma financial information and
exhibits, if any, filed as part of this report.

     (c)  Exhibits.

          Exhibit 20 - Press release dated June 21, 1994.

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                The Exhibit Index appears on Page 4


     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 hereunto duly authorized.

                                   HALLIBURTON COMPANY

Date:     June 29, 1994                 By: (Robert M. Kennedy)
                                             Robert M. Kennedy
                                           Vice President - Legal

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                The Exhibit Index appears on Page 4

                           EXHIBIT INDEX

Exhibit                                           Sequentially
Number              Description                   Numbered Page

    20              Press Release of
                    June 21, 1994                   5-6 of 6
                    Incorporated by Reference

                      Page 4 of 6 pages
                The Exhibit Index appears on Page 4

FOR IMMEDIATE RELEASE              Contact -  Guy T. Marcus
June 21, 1994                           Vice Pres.-Inv. Rel.
                                        (214) 978-2691

              -- HALLIBURTON DRILLING 68 WELLS --

DALLAS, Texas -- Shell Western Exploration and Production Inc.
has launched an extensive coiled-tubing drilling program with
Halliburton Energy Services for 68 injection wells in a
California field.  Based on the number of wells, the project is
likely the world's largest single coiled-tubing drilling program
to date.

With the first 12 wells already completed, Halliburton is now
drilling about one well per day, saving considerable drilling and
rig costs.

The wells are part of a 115-well project in Shell's McKittrick
field near Bakersfield, California.  The field has a complex
system of steam distribution lines, production lines, power lines
and pumping equipment which restrict the space required for
conventional drilling methods.

According to Roy Romagno, Shell's drilling foreman on the
project, the coiled-tubing technology makes it possible to
operate in limited space, without a mast, rotary table and other
equipment necessary for rotary drilling.  Environmentally, he
says, the lower-profile coiled-tubing operation also generates
less noise and emissions and, because of hole size, there are
less cuttings to dispose of.
Halliburton has combined its coiled-tubing equipment and
expertise with its Dyna-drill mud motor technology to offer the
coiled-tubing drilling service in the Shell field.  In the
operation, tubing is fed into the well by an arched injector.
Drilling fluid is circulated down the coiled-tubing, turning the
rotor in a Dyna-drill mud motor and activating the bit.
Halliburton is also providing open-hole logging as part of the
service package.

Gene Rutland, a global coiled-tubing advisor for Halliburton,
says that this is likely the largest single coiled-tubing
drilling project ever undertaken, especially for new wells.  "It
will account," according to Rutland, "for at least one-half of
all the wells drilled this year using coiled-tubing."

The drilling program is expected to last three to four months.
The wells range in depth from 775-960 feet with a total footage
of approximately 61,000.

Halliburton Energy Services, a Halliburton Company organization,
is one of the world's largest suppliers of energy products and
services.  Now in its 75th year, the organization provides a
broad range of services and products to the energy industry

Halliburton Company is one of the world's largest diversified
energy services, engineering, maintenance, and construction
companies.  Founded in 1919, Halliburton provides a broad range
of energy services and products, industrial and marine
engineering and construction services, and property and casualty
insurance services.

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