<PAGE>   1

================================================================================

                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
                            _______________________

                                    FORM S-8

                             REGISTRATION STATEMENT
                                   UNDER THE
                             SECURITIES ACT OF 1933

                        COMMISSION FILE NUMBER: 2-73389

                                 UNICORP, INC.
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)


                NEVADA                                          75-1764386
    (STATE OR OTHER JURISDICTION OF                          (I.R.S. EMPLOYER
     INCORPORATION OR ORGANIZATION)                        IDENTIFICATION NO.)
                                                        
         600 TRAVIS, SUITE 6500                                    77002
             HOUSTON, TEXAS                                     (ZIP CODE)
(ADDRESS OF PRINCIPAL EXECUTIVE OFFICES)

                                 NOT APPLICABLE
                              (FULL TITLE OF PLAN)

      L. MYCHAL JEFFERSON II, 600 TRAVIS, SUITE 6500, HOUSTON, TEXAS 77002
                    (NAME AND ADDRESS OF AGENT FOR SERVICE)

  TELEPHONE NUMBER, INCLUDING AREA CODE, OF AGENT FOR SERVICE: (713) 229-9100

                        CALCULATION OF REGISTRATION FEE

<TABLE>
<CAPTION>
=================================================================================================================
                                                      PROPOSED MAXIMUM        PROPOSED MAXIMUM        AMOUNT OF
TITLE OF EACH CLASS OF SECURITIES   AMOUNT OF SHARES  OFFERING PRICE PER      AGGREGATE OFFERING     REGISTRATION
        TO BE REGISTERED            TO BE REGISTERED        SHARE                  PRICE               FEE (1)
----------------------------------------------------------------------------------------------------------------- 
 <S>                                       <C>              <C>                       <C>           <C>
 COMMON STOCK, PAR
 VALUE $0.01 PER SHARE . . .               50,000           $1.00                     $50,000           $14.75
-----------------------------------------------------------------------------------------------------------------
 TOTAL                                     50,000                                     $50,000           $14.75
=================================================================================================================
</TABLE>
(1) The registration fee applies to all of the shares of the Common Stock to be
    issued as a result of this Registration Statement.


================================================================================
<PAGE>   2
                                    PART II
                          INFORMATION REQUIRED IN THE
                             REGISTRATION STATEMENT

ITEM 3.  INCORPORATION OF DOCUMENTS BY REFERENCE.

         The following documents are incorporated by reference in this
Registration Statement:

         (a)     The Registrant's latest annual report.

         (b)     All other reports filed pursuant to Section 13(a) or 15(d) of
the Securities Exchange Act of 1934 since the end of the fiscal year covered by
the Registrant's latest annual report.

         (c)     The description of the class of securities to be registered by
this Registration Statement, which are registered under Section 12 of the
Securities Act of 1934, and which were more fully described in (i) the Articles
of Incorporation of Texoil, Inc., a Nevada corporation, filed on May 8, 1981
with the Secretary of State of Nevada, and (ii) Certificate of Amendment to
Articles of Incorporation of Texoil, Inc. filed on October 10, 1989 with the
Secretary of State of Nevada, changing the name of Texoil, Inc. to UNICORP,
Inc.

         All documents subsequently filed by the Registrant pursuant to
Sections 13(a), 13(c), 14 and 15(d) of the Securities Exchange Act of 1934,
prior to the filing of a post-effective amendment which indicates that all
securities offered have been sold or which deregisters all securities then
remaining unsold, shall be deemed to be incorporated by reference in the
Registration Statement and to be a part thereof from the date of filing of such
documents.

ITEM 6.  INDEMNIFICATION OF DIRECTORS AND OFFICERS.

         The directors and officers of the Registrant shall be indemnified by
the Registrant against all costs, losses, expenses and liabilities incurred by
any such director or officer in the course of the Registrant's business
according to the Registrant's Articles of Incorporation.  In addition, all
directors and officers are covered by a director's indemnification agreement.

         The foregoing discussion of the Registrant's Articles of Incorporation
is not intended to be exhaustive and is qualified in its entirety by such
document.





                                       1
<PAGE>   3
ITEM 8.  EXHIBITS.  The exhibits listed in the following index are filed as
part of this Registration Statement.  The exhibits indicated by an asterisk (*)
are incorporated by reference.

<TABLE>                                                                      
<CAPTION>                                                                                                              
         EXHIBIT                                                                                                       
         NUMBER                               DESCRIPTION OF EXHIBIT                                                   
         ------                               ----------------------                                                   
          <S>          <C>                                                                                             
          3(a)*        Articles of Incorporation of Texoil, Inc. filed on May 8, 1981 with the Secretary of State of   
                       Nevada, described in the Registration Statement on Form S-2 of the Registrant, effective October
                       13, 1981.  Commission File No. 2-73389.                                                         
                                                                                                                       
          3(b)*        Certificate of Amendment to Articles of Incorporation of Texoil, Inc. filed on October 10, 1989 
                       with the Secretary of State of Nevada, described in Form 10-KSB for the year ended December 31, 
                       1997, filed March 6, 1998.  Commission File No. 2-73389.                                        
                                                                                                                       
          3(c)*        Bylaws, as Amended January 20, 1998, described in Form 10-KSB for the year ended December 31,   
                       1997, filed March 6, 1998.  Commission File No. 2-73389.                                        
                                                                                                                       
            5          Opinion of Norman T. Reynolds, Esq.                                                             
                                                                                                                       
           99.A        Letter Agreement                                                                                
</TABLE>                                                                      

ITEM 9.  UNDERTAKINGS.

         (a)     The undersigned Registrant hereby undertakes:

                 (1)      To file, during any period in which it offers or
sales are being made, a post-effective amendment to this Registration
Statement:

                 (i)      To include any material information with respect to
the plan of distribution not previously disclosed in this Registration
Statement or any material change to such information in this Registration
Statement.

                 (2)      That, for the purpose of determining any liability
under the Securities Act of 1933, each such post-effective amendment shall be
deemed to be a new registration statement relating to the securities offered
therein, and the offering of such securities at that time shall be deemed to be
the initial bona fide offering thereof.

                 (3)      To remove from registration by means of a
post-effective amendment any of the securities being registered which remain
unsold at the termination of the offering.

                 (4)      To file a post-effective amendment to this
Registration Statement to include any financial statements required by Rule
3-19 of Regulation S-X at the start of any delayed offering or throughout a
continuous offering.

         (b)     The undersigned Registrant hereby undertakes that, for
purposes of determining any liability under the Securities Act of 1933, each
filing of the Registrant's annual report pursuant to Section 13(a) or Section
15(d) of the Securities Exchange Act of 1934 (and, where applicable, each
filing of an employee benefit plan's annual report pursuant to Section 15(d) of
the Securities Exchange Act of 1934) that is incorporated by reference in this
Registration Statement shall be deemed to be a new registration statement
relating to the securities offered therein, and the offering of such securities
at that time shall be deemed to be the initial bona fide offering thereof.

         (c)     Insofar as indemnification for liabilities arising under the
Securities Act of 1933 may be permitted to directors, officers and controlling
persons of the Registrant pursuant to the foregoing provisions, or otherwise,
the Registrant has been advised that in the opinion of the Securities and
Exchange Commission such indemnification is against public policy as expressed
in the Act and is, therefore, unenforceable.  In the event that a claim for
indemnification against such liabilities (other than the payment by the
Registrant of expenses incurred or paid by a director, officer or controlling
person of the Registrant in the successful defense of any action, suit or
proceeding) is asserted by such director, officer or controlling person in
connection with the securities being registered, the Registrant will, unless in
the opinion of its counsel the matter has been settled by controlling
precedent, submit to a court of





                                       2
<PAGE>   4
appropriate jurisdiction the question whether such indemnification by it is
against public policy as expressed in the Act and will be governed by the final
adjudication of such issue.

                                   SIGNATURES

         The Registrant.  Pursuant to the requirements of the Securities Act of
1933, the Registrant certifies that it has reasonable grounds to believe that
it meets all of the requirements for filing on Form S-8 and has duly caused
this Registration Statement to be signed on its behalf by the undersigned,
thereunto duly authorized, in Houston, Texas, on March 9, 1998.


                                        UNICORP, INC.



                                        By /s/ L. Mychal Jefferson II
                                          -------------------------------------
                                           L. Mychal Jefferson II, President


         Pursuant to the requirements of the Securities Exchange Act of 1934,
this report has been signed below by the following persons on behalf of the
Registrant and in the capacities and on the dates indicated.

<TABLE>
<CAPTION>
           SIGNATURE                                 TITLE                                   DATE
           ---------                                 -----                                   ----
  <S>                                   <C>                                             <C>
  /s/ Henry A. Schulle                       Chairman of the Board                      March 9, 1998
-------------------------------                                                                      
        Henry A. Schulle

  /s/  L. Mychal Jefferson II                Chief Executive Officer,                   March 9, 1998
-------------------------------             President, Secretary, Chief                              
       L. Mychal Jefferson II            Financial Officer, and Director
</TABLE>





                                       3
<PAGE>   5
                                EXHIBIT INDEX

<TABLE>                                                              
<CAPTION>                                                                                                              
         EXHIBIT                                                                                                       
         NUMBER                               DESCRIPTION OF EXHIBIT                                                   
         ------                               ----------------------                                                   
          <S>          <C>                                                                                             
          3(a)*        Articles of Incorporation of Texoil, Inc. filed on May 8, 1981 with the Secretary of State of   
                       Nevada, described in the Registration Statement on Form S-2 of the Registrant, effective October
                       13, 1981.  Commission File No. 2-73389.                                                         
                                                                                                                       
          3(b)*        Certificate of Amendment to Articles of Incorporation of Texoil, Inc. filed on October 10, 1989 
                       with the Secretary of State of Nevada, described in Form 10-KSB for the year ended December 31, 
                       1997, filed March 6, 1998.  Commission File No. 2-73389.                                        
                                                                                                                       
          3(c)*        Bylaws, as Amended January 20, 1998, described in Form 10-KSB for the year ended December 31,   
                       1997, filed March 6, 1998.  Commission File No. 2-73389.                                        
                                                                                                                       
            5          Opinion of Norman T. Reynolds, Esq.                                                             
                                                                                                                       
           99.A        Letter Agreement                                                                                
</TABLE>
[{"type": "S-8", "sequence": "1", "description": "UNICORP, INC.", "secsgml_size_bytes": 15069}]
{"company-data": {"conformed-name": "UNICORP INC", "cik": "0000354507", "assigned-sic": "1311", "irs-number": "751764386", "state-of-incorporation": "NV", "fiscal-year-end": "1231"}, "filing-values": {"form-type": "S-8", "act": "33", "file-number": "333-47617", "film-number": "98560665"}, "business-address": {"street1": "600 TRAVIS", "street2": "SUITE 6500", "city": "HOUSTON", "state": "TX", "zip": "77002", "phone": "7132299100"}, "mail-address": {"street1": "600 TRAVIS", "street2": "SUITE 6500", "city": "HOUSTON", "state": "TX", "zip": "77002"}}
1

================================================================================

                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
                            _______________________

                                    FORM S-8

                             REGISTRATION STATEMENT
                                   UNDER THE
                             SECURITIES ACT OF 1933

                        COMMISSION FILE NUMBER: 2-73389

                                 UNICORP, INC.
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)

                NEVADA                                          75-1764386
    (STATE OR OTHER JURISDICTION OF                          (I.R.S. EMPLOYER
     INCORPORATION OR ORGANIZATION)                        IDENTIFICATION NO.)
                                                        
         600 TRAVIS, SUITE 6500                                    77002
             HOUSTON, TEXAS                                     (ZIP CODE)
(ADDRESS OF PRINCIPAL EXECUTIVE OFFICES)

                                 NOT APPLICABLE
                              (FULL TITLE OF PLAN)

      L. MYCHAL JEFFERSON II, 600 TRAVIS, SUITE 6500, HOUSTON, TEXAS 77002
                    (NAME AND ADDRESS OF AGENT FOR SERVICE)

  TELEPHONE NUMBER, INCLUDING AREA CODE, OF AGENT FOR SERVICE: (713) 229-9100

                        CALCULATION OF REGISTRATION FEE
=================================================================================================================
                                                      PROPOSED MAXIMUM        PROPOSED MAXIMUM        AMOUNT OF
TITLE OF EACH CLASS OF SECURITIES   AMOUNT OF SHARES  OFFERING PRICE PER      AGGREGATE OFFERING     REGISTRATION
        TO BE REGISTERED            TO BE REGISTERED        SHARE                  PRICE               FEE (1)
-----------------------------------------------------------------------------------------------------------------
COMMON STOCK, PAR
 VALUE $0.01 PER SHARE . . .               50,000           $1.00                     $50,000           $14.75
-----------------------------------------------------------------------------------------------------------------
 TOTAL                                     50,000                                     $50,000           $14.75
=================================================================================================================
(1) The registration fee applies to all of the shares of the Common Stock to be
    issued as a result of this Registration Statement.

================================================================================
2
                                    PART II
                          INFORMATION REQUIRED IN THE
                             REGISTRATION STATEMENT

ITEM 3.  INCORPORATION OF DOCUMENTS BY REFERENCE.

         The following documents are incorporated by reference in this
Registration Statement:

         (a)     The Registrant's latest annual report.

         (b)     All other reports filed pursuant to Section 13(a) or 15(d) of
the Securities Exchange Act of 1934 since the end of the fiscal year covered by
the Registrant's latest annual report.

         (c)     The description of the class of securities to be registered by
this Registration Statement, which are registered under Section 12 of the
Securities Act of 1934, and which were more fully described in (i) the Articles
of Incorporation of Texoil, Inc., a Nevada corporation, filed on May 8, 1981
with the Secretary of State of Nevada, and (ii) Certificate of Amendment to
Articles of Incorporation of Texoil, Inc. filed on October 10, 1989 with the
Secretary of State of Nevada, changing the name of Texoil, Inc. to UNICORP,
Inc.

         All documents subsequently filed by the Registrant pursuant to
Sections 13(a), 13(c), 14 and 15(d) of the Securities Exchange Act of 1934,
prior to the filing of a post-effective amendment which indicates that all
securities offered have been sold or which deregisters all securities then
remaining unsold, shall be deemed to be incorporated by reference in the
Registration Statement and to be a part thereof from the date of filing of such
documents.

ITEM 6.  INDEMNIFICATION OF DIRECTORS AND OFFICERS.

         The directors and officers of the Registrant shall be indemnified by
the Registrant against all costs, losses, expenses and liabilities incurred by
any such director or officer in the course of the Registrant's business
according to the Registrant's Articles of Incorporation.  In addition, all
directors and officers are covered by a director's indemnification agreement.

         The foregoing discussion of the Registrant's Articles of Incorporation
is not intended to be exhaustive and is qualified in its entirety by such
document.

                                       1
3
ITEM 8.  EXHIBITS.  The exhibits listed in the following index are filed as
part of this Registration Statement.  The exhibits indicated by an asterisk (*)
are incorporated by reference.
EXHIBIT                                                                                                       
         NUMBER                               DESCRIPTION OF EXHIBIT                                                   
         ------                               ----------------------
3(a)*        Articles of Incorporation of Texoil, Inc. filed on May 8, 1981 with the Secretary of State of   
                       Nevada, described in the Registration Statement on Form S-2 of the Registrant, effective October
                       13, 1981.  Commission File No. 2-73389.                                                         
                                                                                                                       
          3(b)*        Certificate of Amendment to Articles of Incorporation of Texoil, Inc. filed on October 10, 1989 
                       with the Secretary of State of Nevada, described in Form 10-KSB for the year ended December 31, 
                       1997, filed March 6, 1998.  Commission File No. 2-73389.                                        
                                                                                                                       
          3(c)*        Bylaws, as Amended January 20, 1998, described in Form 10-KSB for the year ended December 31,   
                       1997, filed March 6, 1998.  Commission File No. 2-73389.                                        
                                                                                                                       
            5          Opinion of Norman T. Reynolds, Esq.                                                             
                                                                                                                       
           99.A        Letter Agreement
ITEM 9.  UNDERTAKINGS.

         (a)     The undersigned Registrant hereby undertakes:

                 (1)      To file, during any period in which it offers or
sales are being made, a post-effective amendment to this Registration
Statement:

                 (i)      To include any material information with respect to
the plan of distribution not previously disclosed in this Registration
Statement or any material change to such information in this Registration
Statement.

                 (2)      That, for the purpose of determining any liability
under the Securities Act of 1933, each such post-effective amendment shall be
deemed to be a new registration statement relating to the securities offered
therein, and the offering of such securities at that time shall be deemed to be
the initial bona fide offering thereof.

                 (3)      To remove from registration by means of a
post-effective amendment any of the securities being registered which remain
unsold at the termination of the offering.

                 (4)      To file a post-effective amendment to this
Registration Statement to include any financial statements required by Rule
3-19 of Regulation S-X at the start of any delayed offering or throughout a
continuous offering.

         (b)     The undersigned Registrant hereby undertakes that, for
purposes of determining any liability under the Securities Act of 1933, each
filing of the Registrant's annual report pursuant to Section 13(a) or Section
15(d) of the Securities Exchange Act of 1934 (and, where applicable, each
filing of an employee benefit plan's annual report pursuant to Section 15(d) of
the Securities Exchange Act of 1934) that is incorporated by reference in this
Registration Statement shall be deemed to be a new registration statement
relating to the securities offered therein, and the offering of such securities
at that time shall be deemed to be the initial bona fide offering thereof.

         (c)     Insofar as indemnification for liabilities arising under the
Securities Act of 1933 may be permitted to directors, officers and controlling
persons of the Registrant pursuant to the foregoing provisions, or otherwise,
the Registrant has been advised that in the opinion of the Securities and
Exchange Commission such indemnification is against public policy as expressed
in the Act and is, therefore, unenforceable.  In the event that a claim for
indemnification against such liabilities (other than the payment by the
Registrant of expenses incurred or paid by a director, officer or controlling
person of the Registrant in the successful defense of any action, suit or
proceeding) is asserted by such director, officer or controlling person in
connection with the securities being registered, the Registrant will, unless in
the opinion of its counsel the matter has been settled by controlling
precedent, submit to a court of

                                       2
4
appropriate jurisdiction the question whether such indemnification by it is
against public policy as expressed in the Act and will be governed by the final
adjudication of such issue.

                                   SIGNATURES

         The Registrant.  Pursuant to the requirements of the Securities Act of
1933, the Registrant certifies that it has reasonable grounds to believe that
it meets all of the requirements for filing on Form S-8 and has duly caused
this Registration Statement to be signed on its behalf by the undersigned,
thereunto duly authorized, in Houston, Texas, on March 9, 1998.

                                        UNICORP, INC.

                                        By /s/ L. Mychal Jefferson II
                                          -------------------------------------
                                           L. Mychal Jefferson II, President

         Pursuant to the requirements of the Securities Exchange Act of 1934,
this report has been signed below by the following persons on behalf of the
Registrant and in the capacities and on the dates indicated.
SIGNATURE                                 TITLE                                   DATE
           ---------                                 -----                                   ----
/s/ Henry A. Schulle                       Chairman of the Board                      March 9, 1998
-------------------------------                                                                      
        Henry A. Schulle

  /s/  L. Mychal Jefferson II                Chief Executive Officer,                   March 9, 1998
-------------------------------             President, Secretary, Chief                              
       L. Mychal Jefferson II            Financial Officer, and Director
3
5
                                EXHIBIT INDEX
EXHIBIT                                                                                                       
         NUMBER                               DESCRIPTION OF EXHIBIT                                                   
         ------                               ----------------------
3(a)*        Articles of Incorporation of Texoil, Inc. filed on May 8, 1981 with the Secretary of State of   
                       Nevada, described in the Registration Statement on Form S-2 of the Registrant, effective October
                       13, 1981.  Commission File No. 2-73389.                                                         
                                                                                                                       
          3(b)*        Certificate of Amendment to Articles of Incorporation of Texoil, Inc. filed on October 10, 1989 
                       with the Secretary of State of Nevada, described in Form 10-KSB for the year ended December 31, 
                       1997, filed March 6, 1998.  Commission File No. 2-73389.                                        
                                                                                                                       
          3(c)*        Bylaws, as Amended January 20, 1998, described in Form 10-KSB for the year ended December 31,   
                       1997, filed March 6, 1998.  Commission File No. 2-73389.                                        
                                                                                                                       
            5          Opinion of Norman T. Reynolds, Esq.                                                             
                                                                                                                       
           99.A        Letter Agreement