<PAGE>   1
                                                                    EXHIBIT 1.1



                                  $175,000,000

                              DI INDUSTRIES, INC.
                                 DRILLERS, INC.
                             DI INTERNATIONAL, INC.
                                DI ENERGY, INC.

                          8-7/8% SENIOR NOTES DUE 2007

                             UNDERWRITING AGREEMENT



                                                      June 23, 1997


DONALDSON, LUFKIN & JENRETTE
  SECURITIES CORPORATION
BT SECURITIES CORPORATION
ING BARING (U.S.) SECURITIES, INC.
    as Underwriters
         c/o Donaldson, Lufkin & Jenrette
           Securities Corporation
         277 Park Avenue
         New York, New York 10172

Dear Sirs:

         DI Industries, Inc., a Texas corporation (THE "COMPANY"), Proposes to
issue and sell $175,000,000 principal amount of its 8-7/8% Senior Notes due
2007 (THE "SECURITIES") to the several underwriters named in Schedule I hereto
(the "UNDERWRITERS"). The Securities will be unconditionally guaranteed on a
unsecured senior basis by certain subsidiaries of the Company, Drillers, Inc.,
a Texas corporation, DI International, Inc., a Texas corporation, and DI
Energy, Inc., a Texas corporation (COLLECTIVELY, THE "GUARANTORS"). The
Securities are to be issued pursuant to the provisions of an Indenture to be
dated as of June 27, 1997 (THE "INDENTURE") among the Company, as issuer, the
Guarantors, as guarantors, and Texas Commerce Bank National Association, as
Trustee (THE "TRUSTEE").

         SECTION 1. Registration Statement and Prospectus. The Company and the
Guarantors have prepared and filed with the Securities and Exchange Commission
(THE "COMMISSION") in accordance with the provisions of the Securities Act of
1933, as amended, and the rules and regulations of the Commission thereunder
(COLLECTIVELY, THE "ACT"), a registration statement on Form S-3, including a
prospectus, relating to the Securities. The registration



<PAGE>   2


statement, as amended at the time it became effective, including the
information (if any) deemed to be part of the registration statement at the
time of effectiveness pursuant to Rule 430A under the Act, is hereinafter
referred to as the "REGISTRATION STATEMENT"; and the prospectus in the form
first used to confirm sales of Securities is hereinafter referred to as the
"PROSPECTUS" (including, in the case of all references to the Registration
Statement or the Prospectus, documents incorporated therein by reference). If
the Company and the Guarantors have filed or are required pursuant to the terms
hereof to file a registration statement pursuant to Rule 462(b) under the Act
registering additional Securities (A "RULE 462(B) REGISTRATION STATEMENT"),
then, unless otherwise specified, any reference herein to the term
"Registration Statement" shall be deemed to include such Rule 462(b)
Registration Statement. The terms "SUPPLEMENT" and "AMENDMENT" or "AMEND" as
used in this Agreement with respect to the Registration Statement or the
Prospectus shall include all documents subsequently filed by the Company and/or
the Guarantors with the Commission pursuant to the Securities Exchange Act of
1934, as amended, and the rules and regulations of the Commission thereunder
(COLLECTIVELY, THE "EXCHANGE ACT") that are deemed to be incorporated by
reference in the Prospectus.

         SECTION 2. Agreements to Sell and Purchase. On the basis of the
representations and warranties contained in this Agreement, and subject to its
terms and conditions, the Company agrees to issue and sell, and each
Underwriter agrees, severally and not jointly, to purchase from the Company the
principal amount of Securities set forth opposite the name of such Underwriter
in Schedule I hereto at 96.772% of the principal amount thereof (THE "PURCHASE
PRICE").

         The Company hereby confirms its engagement of Donaldson, Lufkin &
Jenrette Securities Corporation ("DLJ") as, and DLJ hereby confirms its
agreement with the Company to render services as, a "qualified independent
underwriter," within the meaning of Section (b)(15) of Rule 2720 of the
National Association of Securities Dealers, Inc. with respect to the offering
and sale of the Securities. DLJ, solely in its capacity as the qualified
independent underwriter and not otherwise, is referred to herein as the "QIU."
As compensation for the services of the QIU hereunder, the Company agrees to
pay the QIU $5,000 on the Closing Date. The yield on the Securities to be sold
to the public shall not be lower than that recommended by the QIU.

         SECTION 3. Terms of Public Offering. The Company and the Guarantors
are advised by you that the Underwriters propose (i) to make a public offering
of their respective portions of the Securities as soon after the execution and
delivery of this Agreement as in your judgment is advisable and (ii) initially
to offer the Securities upon the terms set forth in the Prospectus.

         SECTION 4. Delivery and Payment. Delivery to the Underwriters of and
payment for the Securities shall be made at 9:00 a.m., New York City time, on
June 27, 1997 (THE "CLOSING DATE") at such place as you shall designate. The


                                       2
<PAGE>   3


Closing Date and the location of delivery of and payment for the Securities may
be varied by agreement among you and the Company.

         Payment of the Purchase Price shall be made to the Company by wire
transfer of immediately available funds to a bank account designated by the
Company against delivery to you for the respective accounts of the several
Underwriters of the Securities with any transfer taxes thereon duly paid by the
Company. The Securities shall be issued in book-entry form through the
facilities of the Depository Trust Company ("DTC"). The Company shall deposit
the global certificate representing the Securities with DTC or its designated
custodian at the Closing Date, and the Company will deliver such global
certificate to the several underwriters by causing DTC to credit the Securities
to the respective accounts of the Underwriters with DTC.

         SECTION 5. Agreements of the Company and the Guarantors. The Company
and the Guarantors agree with you:

         (a) To advise you promptly and, if requested by you, to confirm such
advice in writing, (i) of any request by the Commission for amendments to the
Registration Statement or amendments or supplements to the Prospectus or for
additional information, (ii) of the issuance by the Commission of any stop
order suspending the effectiveness of the Registration Statement or of the
suspension of qualification of the Securities for offering or sale in any
jurisdiction, or the initiation of any proceeding for such purposes, (iii) when
any amendment to the Registration Statement becomes effective, (iv) if the
Company and the Guarantors are required to file a Rule 462(b) Registration
Statement after the effectiveness of this Agreement, when the Rule 462(b)
Registration Statement has become effective and (v) of the happening of any
event during the period referred to in Section 5(d) below which makes any
statement of a material fact made in the Registration Statement or the
Prospectus untrue or which requires any additions to or changes in the
Registration Statement or the Prospectus in order to make the statements
therein not misleading. If at any time the Commission shall issue any stop
order suspending the effectiveness of the Registration Statement, the Company
and the Guarantors will use their best efforts to obtain the withdrawal or
lifting of such order at the earliest possible time.

         (b) To furnish to you, without charge, four signed copies of the
Registration Statement as first filed with the Commission and of each amendment
to it, including all exhibits and documents incorporated therein by reference,
and to furnish to you and each Underwriter designated by you such number of
conformed copies of the Registration Statement as so filed and of each
amendment to it, without exhibits but including all documents incorporated
therein by reference, as you may reasonably request.


                                       3
<PAGE>   4


         (c) To prepare the Prospectus in a form approved by you and to file
the Prospectus in such form with the Commission within the applicable period
specified in Rule 424(b) under the Act; not to file any further amendment to
the Registration Statement and not to make any amendment or supplement to the
Prospectus of which you shall not previously have been advised or to which you
shall reasonably object after being so advised; and to prepare and file with
the Commission, promptly upon your reasonable request, any amendment to the
Registration Statement or amendment or supplement to the Prospectus which may
be necessary or advisable in connection with the distribution of the Securities
by you, and to use its best efforts to cause any such amendment to the
Registration Statement to become promptly effective.

         (d) Prior to 10:00 a.m., New York City time, on the first business day
after the date of this Agreement and from time to time thereafter for such
period as in the opinion of counsel for the Underwriters a prospectus is
required by law to be delivered in connection with sales by an Underwriter or a
dealer, to furnish in New York City to each Underwriter and dealer as many
copies of the Prospectus (and of any amendment or supplement to the Prospectus)
as such Underwriter or dealer may reasonably request.

         (e) If during the period specified in Section 5(d), any event shall
occur as a result of which, in the opinion of counsel for the Underwriters, it
becomes necessary to amend or supplement the Prospectus in order to make the
statements of material facts therein, in the light of the circumstances when
the Prospectus is delivered to a purchaser, not misleading, or if it is
necessary to amend or supplement the Prospectus to comply with applicable law,
forthwith to prepare and file with the Commission an appropriate amendment or
supplement to the Prospectus so that the statements of material facts in the
Prospectus, as so amended or supplemented, will not in the light of the
circumstances when it is so delivered, be misleading, or so that the Prospectus
will comply with applicable law, and to furnish to each Underwriter and to such
dealers as you shall specify, such number of copies thereof as such Underwriter
or dealers may reasonably request.

         (f) Prior to any public offering of the Securities, to cooperate with
you and counsel for the Underwriters in connection with the registration or
qualification of the Securities for offer and sale by the several Underwriters
and by dealers under the state securities or Blue Sky laws of such
jurisdictions as you may request, to continue such qualification in effect so
long as required for distribution of the Securities and to file such consents
to service of process or other documents as may be necessary in order to effect
such registration or qualification; provided, however, that neither the Company
nor any Guarantor



                                       4
<PAGE>   5


shall be required to qualify as a foreign corporation in any jurisdiction in
which it is not already required to be so qualified or to take any action that
would subject it to general consent to service of process in any jurisdiction
in which it is not now so subject.

         (g) To mail and make generally available to its security holders as
soon as practicable an earnings statement covering the twelve-month period
ending June 30, 1998 that shall satisfy the provisions of Section 11(a) of the
Act, and to advise you in writing when such statement has been so made
available.

         (h) So long as the Securities are outstanding, (i) to mail and make
generally available as soon as practicable after the end of each fiscal year to
the record holders of the Securities a financial report of the Company, the
Guarantors and their respective subsidiaries on a consolidated basis (and a
similar financial report of all unconsolidated subsidiaries, if any), all such
financial reports to include a consolidated balance sheet, a consolidated
statement of operations, a consolidated statement of cash flows and a
consolidated statement of shareholders' equity as of the end of and for such
fiscal year, together with comparable information as of the end of and for the
preceding year, certified by independent certified public accountants and (ii)
to mail and make generally available as soon as practicable after the end of
each quarterly period (except for the last quarterly period of each fiscal
year) to such holders, a consolidated balance sheet, a consolidated statement
of operations and a consolidated statement of cash flows (and similar financial
reports of all unconsolidated subsidiaries, if any) as of the end of and for
such period, and for the period from the beginning of such year to the close of
such quarterly period, together with comparable information for the
corresponding periods of the preceding year.

         (i) So long as the Securities are outstanding, to furnish to you as
soon as available copies of all reports or other communications furnished to
its security holders or furnished to or filed with the Commission or any
national securities exchange on which any class of securities of the Company or
any Guarantor is listed and such other publicly available information
concerning the Company, the Guarantors and their respective subsidiaries as you
may reasonably request.

         (j) Whether or not the transactions contemplated in this Agreement are
consummated or this Agreement is terminated, to pay or cause to be paid all
expenses incident to the performance of its obligations under this Agreement,
including: (i) the fees, disbursements and expenses of the Company's counsel
and the Company's accountants in connection with the registration and delivery
of the Securities under the Act and all other fees or expenses in connection
with the preparation, printing, filing and distribution of the Registration
Statement (including financial statements and exhibits), any preliminary
prospectus, the



                                       5
<PAGE>   6


Prospectus and all amendments and supplements to any of the foregoing prior to
or during the period specified in Section 5(d), including the mailing and
delivering of copies thereof to the Underwriters and dealers in the quantities
specified herein, (ii) all costs and expenses related to the transfer and
delivery of the Securities to the Underwriters, including any transfer or other
taxes payable thereon, (iii) all costs of printing or producing this Agreement
and any other agreements or documents in connection with the offering,
purchase, sale or delivery of the Securities, (iv) the costs and charges of any
transfer agent, registrar and/or depositary (including the Depository Trust
Company), (v) the filing fees for the Underwriters in connection with the
review and clearance of the offering of the Securities by the National
Association of Securities Dealers, Inc., (vi) any fees charged by rating
agencies for the rating of the Securities, (vii) the costs of printing
certificates representing the Securities, if any, (viii) the fees of the QIU
specified in Section 2 and (ix) and all other costs and expenses incident to
the performance of the obligations of the Company and the Guarantors hereunder
for which provision is not otherwise made in this Section.

         (k) During the period beginning on the date hereof and continuing to
and including the Closing Date, not to offer, sell, contract to sell or
otherwise transfer or dispose of any debt securities of the Company or any
Guarantor or any warrants, rights or options to purchase or otherwise acquire
debt securities of the Company or any Guarantor substantially similar to the
Securities (other than (i) the Securities and (ii) commercial paper issued in
the ordinary course of business), without the prior written consent of
Donaldson, Lufkin & Jenrette Securities Corporation.

         (l) To use its best efforts to do and perform all things required or
necessary to be done and performed under this Agreement by the Company and the
Guarantors prior to the Closing Date and to satisfy all conditions precedent to
the delivery of the Securities.

         (m) If the Registration Statement at the time of the effectiveness of
this Agreement does not cover all of the Securities, to file a Rule 462(b)
Registration Statement with the Commission registering the Securities not so
covered in compliance with Rule 462(b) by 10:00 p.m., New York City time, on
the date of this Agreement and to pay to the Commission the filing fee for such
Rule 462(b) Registration Statement at the time of the filing thereof or to give
irrevocable instructions for the payment of such fee pursuant to Rule 111(b)
under the Act.

         SECTION 6. Representations and Warranties of the Company and the
Guarantors. The Company and the Guarantors, jointly and severally, represent
and warrant to each Underwriter that:




                                       6
<PAGE>   7


         (a) The Registration Statement has become effective (other than any
Rule 462(b) Registration Statement to be filed by the Company and the
Guarantors after the effectiveness of this Agreement); any Rule 462(b)
Registration Statement filed after the effectiveness of this Agreement will
become effective no later than 10:00 p.m., New York City time, on the date of
this Agreement; and no stop order suspending the effectiveness of the
Registration Statement is in effect, and no proceedings for such purpose are
pending before or threatened by the Commission.

         (b) (i) Each document, if any, filed or to be filed pursuant to the
Exchange Act and incorporated by reference in the Prospectus complied or will
comply when so filed in all material respects with the Exchange Act; (ii) the
Registration Statement (other than any Rule 462(b) Registration Statement to be
filed by the Company and the Guarantors after the effectiveness of this
Agreement), when it became effective, did not contain and, as amended, if
applicable, will not contain any untrue statement of a material fact or omit to
state a material fact required to be stated therein or necessary to make the
statements therein not misleading, the (iii) Registration Statement (other than
any Rule 462(b) Registration Statement to be filed by the Company and the
Guarantors after the effectiveness of this Agreement) and the Prospectus comply
and, as amended or supplemented, if applicable, will comply in all material
respects with the Act, (iv) if the Company and the Guarantors are required to
file a Rule 462(b) Registration Statement after the effectiveness of this
Agreement, such Rule 462(b) Registration Statement and any amendments thereto,
when they become effective (A) will not contain any untrue statement of a
material fact or omit to state a material fact required to be stated therein or
necessary to make the statements therein not misleading and (B) will comply in
all material respects with the Act and (v) the Prospectus does not contain and,
as amended or supplemented, if applicable, will not contain any untrue
statement of a material fact or omit to state a material fact necessary to make
the statements therein, in the light of the circumstances under which they were
made, not misleading, except that the representations and warranties set forth
in this paragraph do not apply to statements or omissions in the Registration
Statement or the Prospectus based upon information relating to any Underwriter
furnished to the Company or any Guarantor in writing by such Underwriter
through you expressly for use therein.

         (c) Each preliminary prospectus filed as part of the registration
statement as originally filed or as part of any amendment thereto, or filed
pursuant to Rule 424 under the Act, complied when so filed in all material
respects with the Act, and did not contain an untrue statement of a material
fact or omit to state a material fact required to be stated therein or
necessary to make the statements therein, in the light of the circumstances
under which they were made, not misleading, except that the representations and
warranties set forth in this



                                       7
<PAGE>   8


paragraph do not apply to statements or omissions in any preliminary prospectus
based upon information relating to any Underwriter furnished to the Company or
any Guarantor in writing by such Underwriter through you expressly for use
therein.

         (d) Each of the Company, the Guarantors and their respective
subsidiaries has been duly formed or incorporated, is validly existing in good
standing under the laws of its jurisdiction of formation or incorporation and
has the corporate or limited liability company power and authority to carry on
its business as described in the Prospectus and to own, lease and operate its
properties, and each is duly qualified and is in good standing as a foreign
entity authorized to do business in each jurisdiction in which the nature of
its business or its ownership or leasing of property requires such
qualification, except where the failure to be so qualified or in good standing
would not have a material adverse effect on the business, prospects, financial
condition or results of operations of the Company, the Guarantors and their
respective subsidiaries, taken as a whole (A "MATERIAL ADVERSE EFFECT").

         (e) All the outstanding shares of capital stock of the Company have
been duly authorized and validly issued and are fully paid and non-assessable.

         (f) All of the outstanding shares of capital stock or other equity
interests of each of the Guarantors and the other subsidiaries of the Company
have been duly authorized and validly issued and are fully paid and
non-assessable, and, except for INDRILLERS, L.L.C. which is a 65%-owned
subsidiary of the Company, are owned by the Company or a subsidiary, as
applicable, free and clear of any security interest, claim, lien, encumbrance
or adverse interest of any nature, other than such as may arise out of or in
connection with the Bank Credit Facility) (as defined in the Prospectus) and
would not have a Material Adverse Effect.

         (g) The Indenture has been duly qualified under the Trust Indenture
Act of 1939, as amended (THE "TRUST INDENTURE ACT"), and has been duly
authorized, executed and delivered by the Company and the Guarantors and is a
valid and binding agreement of the Company and the Guarantors, enforceable in
accordance with its terms except as (A) the enforceability thereof may be
limited by bankruptcy, insolvency, fraudulent conveyance, moratorium or similar
laws, now or hereafter in effect, relating to or affecting creditors' rights
generally and (B) rights of acceleration and the availability of equitable
remedies may be limited by equitable principles of general applicability
(regardless of whether such rights and remedies are sought to be enforced at
law or in equity).

         (h) The Securities have been duly authorized by all necessary
corporate action on the part of the Company and Guarantors and, when executed
and




                                       8
<PAGE>   9


authenticated in accordance with the provisions of the Indenture and delivered
to and paid for by the Underwriters in accordance with the terms of this
Agreement, will be entitled to the benefits of the Indenture and will be valid
and binding obligations of the Company and the Guarantors, enforceable in
accordance with their terms except as (A) the enforceability thereof may be
limited by bankruptcy, insolvency, fraudulent conveyance, moratorium or similar
laws, now or hereafter in effect, relating to or affecting creditors' rights
generally and (B) rights of acceleration and the availability of equitable
remedies may be limited by equitable principles of general applicability
(regardless of whether such rights and remedies are sought to be enforced at
law or in equity).

         (i) The Securities conform, in all material respects, as to legal
matters to the description thereof contained in the Prospectus.

         (j) None of the Company, the Guarantors or any of their respective
subsidiaries is in violation of its respective charter or by-laws or in default
in the performance of any obligation, agreement, covenant or condition
contained in any indenture, loan agreement, mortgage, lease or other agreement
or instrument that, the violation or default of which would have a Material
Adverse Effect, to which the Company, the Guarantors or any of their respective
subsidiaries is a party or by which the Company, the Guarantors or any of their
respective subsidiaries or their respective property is bound.

         (k) The execution, delivery and performance of this Agreement, the
Indenture and the Securities by the Company and the Guarantors, compliance by
the Company and the Guarantors with all the provisions hereof and thereof and
the consummation of the transactions contemplated hereby and thereby will not
require any consent, approval, authorization or other order of, or
qualification with, any court or governmental body or agency (except such as
may be required under the securities or Blue Sky laws of the various states)
and will not conflict with or constitute a breach of any of the terms or
provisions of, or a default under, the charter or by-laws of the Company, the
Guarantors or any of their respective subsidiaries or any indenture, loan
agreement, mortgage, lease or other agreement or instrument to which the
Company, the Guarantors or any of their respective subsidiaries is a party or
by which the Company, the Guarantors or any of their respective subsidiaries or
their respective property is bound, except for any such matters of
non-compliance, conflict, breaches or defaults that would not have a Material
Adverse Effect or violate or conflict with any applicable law or any rule,
regulation, judgment, order or decree of any court or any governmental body or
agency having jurisdiction over the Company, the Guarantors, any of their
respective subsidiaries or their respective property, except for such
violations or conflicts, if any, as would not have a Material Adverse Effect.




                                       9
<PAGE>   10


         (l) There are no legal or governmental proceedings pending, or
threatened, to which the Company, the Guarantors or any of their respective
subsidiaries is, or could be a party, or to which any of their respective
property is, or could be subject, that are required to be described in the
Registration Statement or the Prospectus and are not so described; nor are
there any statutes, regulations, contracts or other documents that are required
to be described in the Registration Statement or the Prospectus or to be filed
as exhibits to the Registration Statement that are not so described or filed as
required.

         (m) None of the Company, the Guarantors or any of their respective
subsidiaries has violated any foreign, federal, state or local law or
regulation relating to the protection of human health and safety, the
environment or hazardous or toxic substances or wastes, pollutants or
contaminants ("ENVIRONMENTAL LAWS") or any provisions of the Employee
Retirement Income Security Act of 1974, as amended, or the rules and
regulations promulgated thereunder, except for such violations which, singly or
in the aggregate, would not have a Material Adverse Effect.

         (n) Each of the Company, the Guarantors and their respective
subsidiaries has such permits, licenses, franchises and authorizations of
governmental or regulatory authorities ("PERMITS"), including, without
limitation, under any applicable Environmental Laws, as are necessary to own,
lease and operate its respective properties and to conduct its business and is
in compliance with all terms and conditions thereof; and no event has occurred
which allows or, after notice or lapse of time or both, would allow, revocation
or termination of such permits or results or, after notice or lapse of time or
both, would result in any other impairment of the rights of the holder of any
such permit; and such permits contain no restrictions that are burdensome to
the Company, the Guarantors or any of their respective subsidiaries; except
where such failure to have, or comply with the terms or conditions of, such
permits, the occurrence of any such event or the presence of any such
restriction would not, singly or in the aggregate, have a Material Adverse
Effect.

         (o) There are no costs or liabilities associated with Environmental
Laws (including, without limitation, any capital or operating expenditures
required for clean-up, closure of properties or compliance with Environmental
Laws or any permit, license or approval, any related constraints on operating
activities and any potential liabilities to third parties) that would, singly
or in the aggregate, have a Material Adverse Effect.

         (p) This Agreement has been duly authorized by all necessary corporate
action, executed and delivered by the Company and the Guarantors.




                                      10
<PAGE>   11


         (q) KPMG Peat Marwick LLP are, and for the years ended December 31,
1994 and 1995, Deloitte & Touche LLP were, independent public accountants with
respect to the Company, the Guarantors and their respective subsidiaries as
required by the Act.

         (r) The consolidated financial statements, together with related
schedules and notes forming part of the Registration Statement and the
Prospectus (and any amendment or supplement thereto), present fairly the
consolidated financial position, results of operations and changes in financial
position of the Company, the Guarantors and their respective subsidiaries on
the basis stated in the Registration Statement at the respective dates or for
the respective periods to which they apply; such statements and related
schedules and notes have been prepared in accordance with generally accepted
accounting principles consistently applied throughout the periods involved,
except as disclosed therein; and the other financial and statistical
information and data set forth in the Registration Statement and the Prospectus
(and any amendment or supplement thereto) is, in all material respects,
accurately presented and prepared on a basis consistent with such financial
statements and the books and records of the Company.

         (s) Neither the Company nor any of the Guarantors is not and, after
giving effect to the offering and sale of the Securities and the application of
the proceeds thereof as described in the Prospectus, will not be, an
"investment company" as such term is defined in the Investment Company Act of
1940, as amended.

         (t) There are no contracts, agreements or understandings between the
Company and any person granting such person the right to require the Company to
include such securities with the Securities registered pursuant to the
Registration Statement.

         (u) Since the date of the most recent balance sheet included in the
Prospectus, other than as set forth in the Prospectus (exclusive of any
amendments or supplements thereto subsequent to the date of this Agreement),
(i) there has not occurred any change having a Material Adverse Effect or any
development that could reasonably be expected to have a Material Adverse
Effect, (ii) there has not been any material adverse change or any development
that could reasonably be expected to have a prospective material adverse change
in the capital stock or in the long-term debt of the Company, the Guarantors or
any of their respective subsidiaries and (iii) none of Company, the Guarantors
or any of its subsidiaries has incurred any material liability or obligation,
direct or contingent.

         (v) The Company and the Guarantors have complied with all provisions
of Section 517.075, Florida Statutes (Chapter 92-198, Laws of Florida).




                                      11
<PAGE>   12


         (w) The Company, the Guarantors and their respective subsidiaries have
good and indefeasible title in fee simple to all real property and good and
indefeasible title to all personal property owned by them which is material to
the business of the Company and its subsidiaries, in each case free and clear
of all liens, encumbrances and defects except such as are described in the
Prospectus or such as do not materially affect the value of such property and
do not interfere with the use made and proposed to be made of such property by
the Company and its subsidiaries; and any real property and building held under
lease by the Company and its subsidiaries are held by them under valid,
subsisting and enforceable leases with such exceptions as are not material and
do not interfere with the use made and proposed to be made of such property and
building by the Company and its subsidiaries, in each case except as described
in the Prospectus.

         (x) The Company, the Guarantors and each of their respective
subsidiaries are insured by insurers of recognized financial responsibility
against such losses and risks and in such amount as are prudent and customary
in the businesses in which they are engaged; and none of the Company, the
Guarantors or any of their respective subsidiaries has any reason to believe
that it will not be able to renew its existing insurance coverage as and when
such coverage expires to obtain similar coverage from similar insurers at a
cost that would not have a Material Adverse Effect.

         (y) The pro forma financial statements of the Company and its
subsidiaries and the related notes thereto set forth in the Registration
Statement and the Prospectus present fairly the information shown therein, have
been prepared in accordance with the applicable requirements of Rule 11-02 of
Regulation S-X promulgated by the Commission and have been compiled on the pro
forma basis described therein; and the assumptions used in the preparation
thereof are reasonable and the adjustments used therein are appropriate to give
effect to the transactions and circumstances referred to therein.

         SECTION 7. Indemnification. (a)(i) Each of the Company and the
Guarantors, jointly and severally, agrees to indemnify and hold harmless each
Underwriter, its directors, its officers and each person, if any, who controls
any Underwriter within the meaning of Section 15 of the Act or Section 20 of
the Exchange Act from and against any and all losses, claims, damages,
liabilities and judgments (including, without limitation, any legal or other
expenses incurred in connection with defending or investigating any matter,
including any action, that could give rise to any such losses, claims, damages,
liabilities or judgments) caused by any untrue statement or alleged untrue
statement of a material fact contained in the Registration Statement (or any
amendment thereto), the Prospectus (or any amendment or supplement thereto) or
any preliminary



                                      12
<PAGE>   13


prospectus, or caused by any omission or alleged omission to state therein a
material fact required to be stated therein or necessary to make the statements
therein not misleading, except insofar as such losses, claims, damages,
liabilities or judgments are caused by any such untrue statement or omission or
alleged untrue statement or omission based upon information relating to any
Underwriter furnished in writing to the Company and the Guarantors by such
Underwriter through you expressly for use therein and (ii) each of the Company
and the Guarantors, jointly and severally, agrees to indemnify and hold
harmless the QIU, its directors, its officers and each person, if any, who
controls the QIU within the meaning of Section 15 of the Act or Section 20 of
the Exchange Act (A "QIU INDEMNIFIED PARTY"), from and against any and all
losses, claims, damages, liabilities and judgments (including, without
limitation, any legal or other expenses incurred in connection with defending
or investigating any matter, including any action, that could give rise to any
such losses, claims, damages, liabilities or judgments) related to, based upon
or arising out of (i) any untrue statement or alleged untrue statement of a
material fact contained in the Registration Statement (or any amendment
thereto), the Prospectus (or any amendment or supplement thereto) or any
preliminary prospectus, or any omission or alleged omission to state therein a
material fact required to be stated therein or necessary to make the statements
therein not misleading or (ii) the QIU's activities as QIU under its engagement
pursuant to Section 2 hereof, except in the case of this clause (ii) insofar as
any such losses, claims, damages, liabilities or judgments are found in a final
judgment by a court of competent jurisdiction, not subject to further appeal,
to have resulted solely from the willful misconduct or gross negligence of the
QIU.

         (b) Each Underwriter agrees, severally and not jointly, to indemnify
and hold harmless the Company, the Guarantors and their respective directors
and officers who sign the Registration Statement and any person controlling the
Company or any Guarantor within the meaning of Section 15 of the Act or Section
20 of the Exchange Act, to the same extent as the foregoing indemnity from the
Company and the Guarantors to such Underwriter but only with reference to
information relating to such Underwriter furnished in writing to the Company by
such Underwriter through you expressly for use in the Registration Statement
(or any amendment thereto), the Prospectus (or any amendment or supplement
thereto) or any preliminary prospectus.

         (c) In case any action shall be commenced involving any person in
respect of which indemnity may be sought pursuant to Section 7(a) or 7(b) (the
"INDEMNIFIED PARTY"), the indemnified party shall promptly notify the person
against whom such indemnity may be sought (the "INDEMNIFYING PARTY") in writing
and the indemnifying party shall assume the defense of such action, including
the employment of counsel reasonably satisfactory to the indemnified




                                      13
<PAGE>   14


party and the payment of all fees and expenses of such counsel, as incurred
(except that in the case of any action in respect of which indemnity may be
sought pursuant to both Sections 7(a) and 7(b), the Underwriter shall not be
required to assume the defense of such action pursuant to this Section 7(c),
but may employ separate counsel and participate in the defense thereof, but the
fees and expenses of such counsel, except as provided below, shall be at the
expense of such Underwriter). Any indemnified party shall have the right to
employ separate counsel in any such action and participate in the defense
thereof, but the fees and expenses of such counsel shall be at the expense of
the indemnified party unless (i) the employment of such counsel shall have been
specifically authorized in writing by the indemnifying party, (ii) the
indemnifying party shall have failed to assume the defense of such action or
employ counsel reasonably satisfactory to the indemnified party or (iii) the
named parties to any such action (including any impleaded parties) include both
the indemnified party and the indemnifying party, and the indemnified party
shall have been advised by counsel selected by the indemnifying party that
there may be one or more legal defenses available to it which are different
from or additional to those available to the indemnifying party and that, as a
matter of professional responsibility, such counsel is unable to represent both
the indemnifying and indemnified party (in which case the indemnifying party
shall not have the right to assume the defense of such action on behalf of the
indemnified party). In any such case, the indemnifying party shall not, in
connection with any one action or separate but substantially similar or related
actions in the same jurisdiction arising out of the same general allegations or
circumstances, be liable for the fees and expenses of more than one separate
firm of attorneys (in addition to any local counsel) for all indemnified
parties and all such fees and expenses shall be reimbursed as they are
incurred. Such firm shall be designated in writing by Donaldson, Lufkin &
Jenrette Securities Corporation, in the case of parties indemnified pursuant to
Section 7(a), and by the Company, in the case of parties indemnified pursuant
to Section 7(b). The indemnifying party shall indemnify and hold harmless the
indemnified party from and against any and all losses, claims, damages,
liabilities and judgments by reason of any settlement of any action only if
such settlement is (i) effected with its written consent or (ii) effected in
good faith without its written consent if the settlement is entered into more
than 30 days after the indemnifying party shall have received a request from
the indemnified party for reimbursement for the fees and expenses of counsel
(in any case where such fees and expenses are at the expense of the
indemnifying party) and, prior to the date of such settlement, the indemnifying
party shall have failed to comply with such reimbursement request unless within
30 days after such reimbursement request is received, the indemnifying party
shall have made a good faith written challenge to the reasonableness of the
amount or nature of the reimbursement requested or the sufficiency of the
documentation supporting the reimbursement requested (which challenge shall set
forth the amount or nature of the requested reimbursement




                                      14
<PAGE>   15


which the indemnifying party in good faith believes to be reasonable or the
basis for the good faith claim as to the insufficiency of any supporting
documentation), in which event this clause (ii) shall apply only if, and to the
extent that, such indemnifying party shall not have reimbursed the indemnified
party for the amount which is not being so challenged. No indemnifying party
shall, without the prior written consent of the indemnified party, effect any
settlement or compromise of, or consent to the entry of judgment with respect
to, any pending or threatened action in respect of which the indemnified party
is or could have been a party and indemnity or contribution may be or could
have been sought hereunder by the indemnified party, unless such settlement,
compromise or judgment (i) includes an unconditional release of the indemnified
party from all liability on claims that are or could have been the subject
matter of such action and (ii) does not include a statement as to or an
admission of fault, culpability or a failure to act, by or on behalf of the
indemnified party.

         (d) To the extent the indemnification provided for in this Section 7
is unavailable to an indemnified party or insufficient in respect of any
losses, claims, damages, liabilities or judgments referred to therein, then
each indemnifying party, in lieu of indemnifying such indemnified party, shall
contribute to the amount paid or payable by such indemnified party as a result
of such losses, claims, damages, liabilities and judgments (i) in such
proportion as is appropriate to reflect the relative benefits received by the
Company and the Guarantors on the one hand and the Underwriters on the other
hand from the offering of the Securities or (ii) if the allocation provided by
clause 7(d)(i) above is not permitted by applicable law, in such proportion as
is appropriate to reflect not only the relative benefits referred to in clause
7(d)(i) above but also the relative fault of the Company and the Guarantors and
the Underwriters in connection with the statements or omissions which resulted
in such losses, claims, damages, liabilities or judgments, as well as any other
relevant equitable considerations. The relative benefits received by the
Company and the Guarantors and the Underwriters shall be deemed to be in the
same proportion as the total net proceeds from the offering (before deducting
expenses) received by the Company and the Guarantors, and the total
underwriting discounts and commissions received by the Underwriters, bear to
the total price to the public of the Securities, in each case as set forth in
the table on the cover page of the Prospectus. The relative fault of the
Company and the Guarantors and the Underwriters shall be determined by
reference to, among other things, whether the untrue or alleged untrue
statement of a material fact or the omission or alleged omission to state a
material fact relates to information supplied by the Company and the Guarantors
or the Underwriters and the parties' relative intent, knowledge, access to
information and opportunity to correct or prevent such statement or omission.




                                      15
<PAGE>   16



         The Company, the Guarantors and the Underwriters agree that it would
not be just and equitable if contribution pursuant to this Section 7(d) were
determined by pro rata allocation (even if the Underwriters were treated as one
entity for such purpose) or by any other method of allocation which does not
take account of the equitable considerations referred to in the immediately
preceding paragraph. The amount paid or payable by an indemnified party as a
result of the losses, claims, damages, liabilities or judgments referred to in
the immediately preceding paragraph shall be deemed to include, subject to the
limitations set forth above, any legal or other expenses incurred by such
indemnified party in connection with investigating or defending any matter that
could have given rise to such losses, claims, damages, liabilities or
judgments. Notwithstanding the provisions of this Section 7, no Underwriter
shall be required to contribute any amount in excess of the amount by which the
total price at which the Securities underwritten by it and distributed to the
public were offered to the public exceeds the amount of any damages which such
Underwriter has otherwise been required to pay by reason of such untrue or
alleged untrue statement or omission or alleged omission. No person guilty of
fraudulent misrepresentation (within the meaning of Section 11(f) of the Act)
shall be entitled to contribution from any person who was not guilty of such
fraudulent misrepresentation. The Underwriters' obligations to contribute
pursuant to this Section 7(d) are several in proportion to the respective
principal amount of Securities purchased by each of the Underwriters hereunder
and not joint.

         (e) The remedies provided for in this Section 7 are not exclusive and
shall not limit any rights or remedies which may otherwise be available to any
indemnified party, including, without limitation, any QIU Indemnified Party, at
law or in equity.

         SECTION 8. Conditions of Underwriters' Obligations. The several
obligations of the Underwriters to purchase the Securities under this Agreement
are subject to the satisfaction of each of the following conditions:

         (a) All the representations and warranties of the Company and the
Guarantors contained in this Agreement shall be true and correct on the Closing
Date with the same force and effect as if made on and as of the Closing Date.

         (b) If the Company is required to file a Rule 462(b) Registration
Statement after the effectiveness of this Agreement, such Rule 462(b)
Registration Statement shall have become effective by 10:00 p.m., New York City
time, on the date of this Agreement; and no stop order suspending the
effectiveness of the Registration Statement shall have been issued and no
proceedings for that purpose shall have been commenced or shall be pending
before or contemplated by the Commission.




                                      16
<PAGE>   17


         (c) On or after the date hereof there shall not have occurred any
downgrading, nor shall any notice have been given of any intended or potential
downgrading or of any review for a possible change that does not indicate the
direction of the possible change, in the rating of any of the Company's
securities (including, without limitation, the placing of any securities on
negative or developing watch or negative or developing outlook) by any
"nationally recognized statistical rating organization" as such term is defined
for purposes of Rule 436(g)(2) under the Act.

         (d) You shall have received on the Closing Date a certificate dated
the Closing Date, signed by Thomas P. Richards and T. Scott O'Keefe, in their
capacities as the Chief Executive Officer and Chief Financial Officer,
respectively, of each of the Company and the Guarantors, confirming the matters
set forth in Sections 8(a), 8(b) and 8(c).

         (e) Since the date of the most recent balance sheet in the Prospectus
other than as set forth in the Prospectus (exclusive of any amendments or
supplements thereto subsequent to the date of this Agreement), (i) there shall
not have occurred any change having a Material Adverse Effect or any
development that could reasonably be expected to have a Material Adverse
Effect, (ii) there shall not have been any material adverse change or any
development involving a prospective material adverse change in the capital
stock or in the long-term debt of the Company, the Guarantors or any of their
respective subsidiaries and (iii) none of the Company, the Guarantors or any of
its subsidiaries shall have incurred any liability or obligation, direct or
contingent, the effect of which, in any such case described in clause 8(e)(i),
(ii) or (iii), in your judgment, is material and adverse and, in your judgment,
makes it impractical to market the Securities on the terms and in the manner
contemplated by the Prospectus.

         (f) You shall have received on the Closing Date an opinion
(satisfactory to you and counsel for the Underwriters), dated the Closing Date,
of Porter & Hedges L.L.P., counsel for the Company and the Guarantors in
substantially the form set forth in Schedule II.

          (g) You shall have received on the Closing Date an opinion, dated the
Closing Date, of Akin, Gump, Strauss, Hauer & Feld, L.L.P., counsel for the
Underwriters, as to certain matters agreed between you and such counsel.

          (h) You shall have received, on each of the date hereof and the
Closing Date, a letter dated the date hereof or the Closing Date, as the case
may be, in form and substance satisfactory to you, from KPMG Peat Marwick LLP
and Deloitte & Touche LLP, independent public accountants, containing the



                                      17
<PAGE>   18


information and statements of the type ordinarily included in accountants'
"comfort letters" to Underwriters with respect to the financial statements and
certain financial information contained in the Registration Statement and the
Prospectus.

         (i) The Securities are rated "B+" by Standard & Poor's Corporation and
"B1" by Moody's Investors Service, Inc.

         (j) The Company or any Guarantor shall not have failed at or prior to
the Closing Date to perform or comply with any of the agreements herein
contained and required to be performed or complied with by the Company or any
Guarantor at or prior to the Closing Date.

         (k) You shall have received an opinion of Venezuelan counsel to the
Company substantially in the form attached as Schedule III hereto.

         (l) All conditions precedent to the closing of the Grey Wolf
Acquisition (as defined in the Prospectus) shall have been satisfied or waived,
except for the payment of the purchase price by the Company, which shall be
paid contemporaneously with the Closing.

         SECTION 9. Effectiveness of Agreement and Termination. This Agreement
shall become effective upon the execution and delivery of this Agreement by the
parties hereto.

         This Agreement may be terminated at any time prior to the Closing Date
by you by written notice to the Company and the Guarantors if any of the
following has occurred: (i) any outbreak or escalation of hostilities or other
national or international calamity or crisis or change in economic conditions
or in the financial markets of the United States or elsewhere that, in your
judgment, is material and adverse and would, in your judgment, make it
impracticable to market the Securities on the terms and in the manner
contemplated in the Prospectus, (ii) the suspension or material limitation of
trading in securities on the New York Stock Exchange, the American Stock
Exchange, the Chicago Board of Options Exchange, the Chicago Mercantile
Exchange, the Chicago Board of Trade or the Nasdaq National Market or
limitation on prices for securities on any such exchange or the Nasdaq National
Market, (iii) the suspension of trading of any securities of the Company on any
exchange or in the over-the-counter market, (iv) the enactment, publication,
decree or other promulgation of any federal or state statute, regulation, rule
or order of any court or other governmental authority which in your opinion
materially and adversely affects, or will materially and adversely affect, the
business, prospects, financial condition or results of operations of the
Company, the Guarantors and their respective subsidiaries, taken




                                      18
<PAGE>   19


as a whole, (v) the declaration of a banking moratorium by either federal or
New York State authorities or (vi) the taking of any action by any federal,
state or local government or agency in respect of its monetary or fiscal
affairs which in your opinion has a material adverse effect on the financial
markets in the United States and would, in your opinion, make it impracticable
or inadvisable to market the Securities.

         If on the Closing Date any one or more of the Underwriters shall fail
or refuse to purchase the Securities which it or they have agreed to purchase
hereunder on such date and the aggregate principal amount of Securities which
such defaulting Underwriter or Underwriters, as the case may be, agreed but
failed or refused to purchase is not more than one-tenth of the aggregate
principal amount of Securities to be purchased on such date by all
Underwriters, each non-defaulting Underwriter shall be obligated severally, in
the proportion which the principal amount of Securities set forth opposite its
name in Schedule I bears to the aggregate principal amount of Securities which
all the non-defaulting Underwriters, as the case may be, have agreed to
purchase, or in such other proportion as you may specify, to purchase the
Securities which such defaulting Underwriter or Underwriters, as the case may
be, agreed but failed or refused to purchase on such date; provided that in no
event shall the aggregate principal amount of Securities which any Underwriter
has agreed to purchase pursuant to Section 2 hereof be increased pursuant to
this Section 10 by an amount in excess of one-ninth of such principal amount of
Securities without the written consent of such Underwriter. If on the Closing
Date any Underwriter or Underwriters shall fail or refuse to purchase
Securities and the aggregate principal amount of Securities with respect to
which such default occurs is more than one-tenth of the aggregate principal
amount of Securities to be purchased by all Underwriters and arrangements
satisfactory to you and the Company for purchase of such Securities are not
made within 48 hours after such default, this Agreement will terminate without
liability on the part of any non-defaulting Underwriter and the Company. In any
such case which does not result in termination of this Agreement, either you or
the Company shall have the right to postpone the Closing Date, but in no event
for longer than seven days, in order that the required changes, if any, in the
Registration Statement and the Prospectus or any other documents or
arrangements may be effected. Any action taken under this paragraph shall not
relieve any defaulting Underwriter from liability in respect of any default of
any such Underwriter under this Agreement.

         SECTION 10. Miscellaneous. Notices given pursuant to any provision of
this Agreement shall be addressed as follows: (i) if to the Company to, or the
Guarantors c/o, DI Industries, Inc., 10370 Richmond Avenue, Suite 600, Houston,
Texas 77042, Attn: Chief Financial Officer, and (ii) if to any Underwriter or
to you, to you c/o Donaldson, Lufkin & Jenrette Securities Corporation, 277
Park




                                      19
<PAGE>   20


Avenue, New York, New York 10172, Attention: Syndicate Department, or in any
case to such other address as the person to be notified may have requested in
writing.

         The respective indemnities, contribution agreements, representations,
warranties and other statements of the Company, the Guarantors and the several
Underwriters set forth in or made pursuant to this Agreement shall remain
operative and in full force and effect, and will survive delivery of and
payment for the Securities, regardless of (i) any investigation, or statement
as to the results thereof, made by or on behalf of any Underwriter, any QIU
Indemnified Party, the officers or directors of any Underwriter, any person
controlling any Underwriter, the Company, the Guarantors, the officers or
directors of the Company and the Guarantors or any person controlling the
Company and the Guarantors, (ii) acceptance of the Securities and payment for
them hereunder and (iii) termination of this Agreement.

         If for any reason the Securities are not delivered by or on behalf of
the Company as provided herein (other than as a result of any termination of
this Agreement pursuant to Section 9), the Company agrees to reimburse the
several Underwriters for all out-of-pocket expenses (including the fees and
disbursements of counsel) reasonably incurred by them.

         Except as otherwise provided, this Agreement has been and is made
solely for the benefit of and shall be binding upon the Company, the
Guarantors, the Underwriters, the Underwriters' directors and officers, any
controlling persons referred to herein, QIU Indemnified Parties, the directors
and officers of the Company and the Guarantors who sign the Registration
Statement and their respective successors and assigns, all as and to the extent
provided in this Agreement, and no other person shall acquire or have any right
under or by virtue of this Agreement. The term "successors and assigns" shall
not include a purchaser of any of the Securities from any of the several
Underwriters merely because of such purchase.

         This Agreement shall be governed and construed in accordance with the
laws of the State of New York.

         This Agreement may be signed in various counterparts which together
shall constitute one and the same instrument.


                                      20
<PAGE>   21





         Please confirm that the foregoing correctly sets forth the agreement
between the Company, the Guarantors, the several Underwriters and the QIU.

                                        Very truly yours,

                                        DI INDUSTRIES, INC.

                                        By:  /s/ T. P. Richards
                                             ----------------------------------
                                        Name:   Thomas P. Richards
                                                -------------------------------
                                        Title:  President and Chief 
                                                -------------------------------
                                                Executive Officer
                                                -------------------------------

                                        DRILLERS, INC.

                                        By:  /s/ T. P. Richards
                                             ----------------------------------
                                        Name:   Thomas P. Richards
                                                -------------------------------
                                        Title:  President and 
                                                -------------------------------
                                                Chief Executive Officer
                                                -------------------------------

                                        DI INTERNATIONAL, INC.

                                        By:  /s/ T. P. Richards
                                             ----------------------------------
                                        Name:   Thomas P. Richards
                                                -------------------------------
                                        Title:   President and
                                                 ------------------------------
                                                 Chief Executive Officer
                                                 ------------------------------


                                        DI ENERGY, INC.

                                        By:  /s/ T. P. Richards
                                             ----------------------------------
                                        Name:   Thomas P. Richards
                                                -------------------------------
                                        Title:  President and 
                                                -------------------------------
                                                Chief Executive Officer
                                                -------------------------------


                              Signature Page - 1
<PAGE>   22


DONALDSON, LUFKIN & JENRETTE
  SECURITIES CORPORATION
BT SECURITIES CORPORATION
ING BARING (U.S.) SECURITIES, INC.
   as Underwriters

By: DONALDSON, LUFKIN & JENRETTE
         SECURITIES CORPORATION

By:  /s/ Craig Klaasmeyer
     -----------------------------
Name:  Craig Klaasmeyer
      ----------------------------
Title:  Vice President
      ----------------------------

DONALDSON, LUFKIN & JENRETTE
  SECURITIES CORPORATION
     as Qualified Independent Underwriter

By:  /s/ Craig Klaasmeyer
     ------------------------------
Name:  Craig Klaasmeyer
      -----------------------------
Title:  Vice President
      -----------------------------


                              Signature Page - 2

<PAGE>   23







                                   SCHEDULE I

<TABLE>
<CAPTION>
                                                             Principal Amount
                                                              of Securities
Underwriters                                                 to be Purchased
------------                                                 ---------------
<S>                                                           <C>         
Donaldson, Lufkin & Jenrette Securities Corporation           $105,000,000
BT Securities Corporation                                       52,500,000
ING Baring (U.S.) Securities, Inc.                              17,500,000
                                                              ------------
                                      Total                   $175,000,000
                                                              ============
</TABLE>