<PAGE>   1
================================================================================
     As filed with the Securities and Exchange Commission on June 15, 1998
                                                                 File No. 33-



                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                           --------------------------
                                    FORM S-8
                             REGISTRATION STATEMENT
                                     Under
                           THE SECURITIES ACT OF 1933
                           --------------------------

                           Anixter International Inc.
             (Exact Name of Registrant as Specified in its Charter)


            Delaware                                     94-1658138
  (State or Other Jurisdiction              (I.R.S. Employer Identification No.)
of Incorporation or Organization)   


        4711 Golf Road
            Skokie, Illinois                               60076
(Address of Principal Executive Offices)                  (Zip Code)


                           ANIXTER INTERNATIONAL INC.
                           1998 Stock Incentive Plan
                            (Full Title of the Plan)

                                   John Dul
                                4711 Golf Road
                            Skokie, Illinois  60076
                    (Name and Address of Agent For Service)

                                 (847) 677-2600
         (Telephone Number, Including Area Code, of Agent For Service)

                        -------------------------------

                        CALCULATION OF REGISTRATION FEE

<TABLE>
<CAPTION>
========================================================================================================================
                                       Amount               Proposed              Proposed Maximum          Amount of
       Title of Securities             to be            Maximum Offering         Aggregate Offering       Registration
         to be Registered            Registered        Price Per Share(1)             Price(1)                 Fee
  <S>                                <C>                  <C>                        <C>                    <C>
------------------------------------------------------------------------------------------------------------------------
  Common Stock ($1.00 per             3,000,000           $18.125                   $54,375,000            $16,041
  share par value)............        shares              
========================================================================================================================
</TABLE>


(1)  Estimated solely for the purpose of calculating the registration fee
     pursuant to Rule 457(h) on the basis of the average of the high and low
     prices as reported on the Composition Tape for the New York Stock Exchange
     on June 12, 1998.
<PAGE>   2
                                    Part II

                            INFORMATION REQUIRED IN
                           THE REGISTRATION STATEMENT

ITEM 3.   INCORPORATION OF DOCUMENTS BY REFERENCE.

      The following documents, which have heretofore been filed by Anixter
International Inc., a Delaware corporation (the "Company"), with the Securities
and Exchange Commission (the "Commission") pursuant to the Securities Act of
1933, as amended (the "Securities Act"), and the Securities Exchange Act of
1934, as amended (the "Exchange Act"), are incorporated by reference herein and
shall be deemed to be a part hereof:

      (a) The Company's Annual Report on Form 10-K for the year ended 
          January 2, 1998.

      (b) The description of the Company's Common Stock under the caption
          "Description of Registrant's Securities to be Registered" included in
          the Company's Registration Statement No. 33-12390 dated March 4,
          1987.
        
      (c) The Company's Quarterly Report on Form 10-Q for the 13 weeks ended
          April 3, 1998.

      All documents subsequently filed by the Company pursuant to Section
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 herein by reference and shall be
deemed a part hereof from the date of filing of such documents.

ITEM 4.   DESCRIPTION OF SECURITIES.

      Not applicable.

ITEM 5.   INTERESTS OF NAMED EXPERTS AND COUNSEL.

      Certain Legal matters with respect to the legality of the Common Stock
offered hereby will be passed upon for the Company by James E. Knox, Senior
Vice President-Law and Secretary of the Company.  Mr. Knox holds a total of 
approximately 562,000 shares and options to acquire shares of Common Stock.

ITEM 6.   INDEMNIFICATION OF DIRECTORS AND OFFICERS.

      Section 145 of the Delaware General Corporation Law (the "DGCL") and
Article IX of the Company's By-laws authorize and empower the Company to
indemnify the directors, officers, employees and agents of the Company against
liabilities incurred in connection with, and related expenses resulting from,
any claim, action or suit brought against any such person as a result of his
relationship with the Company, provided that such persons acted in accordance
with a stated standard of conduct in connection with the acts or events on
which such claim, action or suit is





                                       2
<PAGE>   3
based.  The finding of either civil or criminal liability on the part of such
persons in connection with such acts or events is not necessarily determinative
of the questions of whether such persons have met the required standard of
conduct and are, accordingly, entitled to be indemnified.

      In addition, Article IX of the Company's Restated Certificate of
Incorporation, as amended, provides that the Company's directors do not have
personal liability to the Company or its stockholders for monetary damages for
any breach of their fiduciary duty as directors except (i) for a breach of the
duty of loyalty, (ii) for acts or omissions not in good faith or which involve
intentional misconduct or knowing violation of the law, (iii) for willful or
negligent violations of certain provisions in the DGCL imposing certain
requirements with respect to stock repurchases, redemptions and dividends or
(iv) for any transaction from which the director derived an improper personal
benefit.  Subject to these exceptions, under Article IX directors do not have
any personal liability to the Company or its stockholders for any violation of
their fiduciary duty.

      The Company has entered into indemnification agreements with each of its
directors and officers (the "Indemnification Agreements").  The Indemnification
Agreements provide for the prompt indemnification "to the fullest extent
permitted by law" and for the prompt advancement of expenses, including
attorney's fees and other costs, expenses and obligations paid or incurred in
connection with investigating, defending, being a witness or participating in
(including on appeal) any threatened, pending or completed action, suit or
proceeding related to the fact that such director or officer is or was a
director, officer, employee, trustee, agent or fiduciary of the Company or is
or was serving at the request of the Company as a director, officer, employee,
trustee, agent or fiduciary of another corporation, partnership, joint venture,
employee benefit plan, trust or other enterprise, or by reason of anything done
by a director in any such capacity.  The Indemnification Agreements further
provide that the Company has the burden of providing that a director or officer
is not entitled to indemnification in any particular case.

      The Company has purchase insurance policies that, if any officer or
director of the Company or its subsidiaries becomes legally obligated to make a
payment (including legal fees and expenses) in connection with an alleged
wrongful act, the insurer will reimburse such officers and directors if the
indemnification payments, as provided above, are not made by the Company or its
subsidiaries to such officers and directors.  Wrongful act means any breach of
duty, neglect, error, misstatement, misleading statement or other act done by
an officer or director of the Company or any subsidiary.

ITEM 7.   EXEMPTION FROM REGISTRATION CLAIMED.

      Not applicable.

ITEM 8.   EXHIBITS.

      See Exhibit Index which is incorporated herein by reference.





                                       3
<PAGE>   4
ITEM 9.   UNDERTAKINGS.

      The undersigned registrant hereby undertakes:

          1.      To file, during any period in which offers or sales are being
                  made, a post-effective amendment to this registration
                  statement:

                  (i)      To include any prospectus required by section
                           10(a)(3) of the Securities Act of 1933;

                  (ii)     To reflect in the prospectus any facts or events
                           arising after the effective date of the registration
                           statement (or the most recent post-effective
                           amendment thereof) which, individually or in the
                           aggregate, represent a fundamental change in the
                           information set forth in the registration statement;

                  (iii)    To include any material information with respect to
                           the plan of distribution not previously disclosed in
                           the registration statement or any material change to
                           such information in the registration statement;

                           Provided, however, that paragraphs (1)(i) and
                           (1)(ii) do not apply if the registration statement
                           is on Form S-3 or Form S-8, and the information
                           required to be included in a post- effective
                           amendment by those paragraphs is contained in
                           periodic reports filed by the registrant pursuant to
                           section 13 or section 15(d) of the Securities
                           Exchange Act of 1934 that are incorporated by
                           reference in the 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.

          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 the
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.





                                       4
<PAGE>   5

      Pursuant to the requirements of the Securities Act of 1933, the
registrant certifies that it has duly caused this registration statement, or
amendment thereto, to be signed on its behalf by the undersigned, thereunto
duly authorized, in the City of Chicago, State of Illinois on June 12, 1998.

                        Anixter International Inc.
                   
                   
                            /s/       James E. Knox                    
                        -----------------------------------------------
                                      James E. Knox
                         Senior Vice President-Law and Secretary


     PURSUANT TO THE REQUIREMENTS OF THE SECURITIES EXCHANGE ACT OF 1933, THIS
REGISTRATION STATEMENT HAS BEEN SIGNED BELOW ON JUNE 10, 1996 BY THE FOLLOWING
PERSONS ON BEHALF OF THE REGISTRANT IN THE CAPACITIES INDICATED.


               LORD JAMES BLYTH*                        Director
---------------------------------------                         
               Lord James Blyth          
                                         
               ROD F. DAMMEYER*                         Director               
---------------------------------------                                        
               Rod F. Dammeyer                        
                                         
               ROBERT E. FOWLER, JR.*                   Director  
---------------------------------------                         
               Robert E. Fowler, Jr.     
                                         
     /s/       JAMES M. FROISLAND               Vice President-Controller
---------------------------------------                                  
               James M. Froisland        
                                         
     /s/       ROBERT W. GRUBBS            President, Chief Executive Officer, 
---------------------------------------               and Director             
               Robert W. Grubbs          
                                         
               F. PHILIP HANDY*                         Director
----------------------------------------                        
               F. Philip Handy           
                                         
               MELVYN N. KLEIN*                         Director
----------------------------------------                        
               Melvyn N. Klein           
                                         
   /s/         DENNIS J. LETHAM                Sr. Vice President-Finance and
---------------------------------------            Chief Financial Officer
               Dennis J. Letham                  
                                         
                JOHN R. PETTY*                          Director
---------------------------------------                         
                John R. Petty            
                                         
               SHELI Z. ROSENBERG*                      Director
---------------------------------------                         
              Sheli Z. Rosenberg              



                                       5
<PAGE>   6
          STUART M. SLOAN*                    Director
----------------------------------------              
          Stuart M. Sloan               
                                        
          THOMAS C. THEOBALD*                 Director
----------------------------------------              
          Thomas C. Theobald            
                                        
          SAM ZELL*                           Director
----------------------------------------              
          Sam Zell                      
                                        

*By        /s/    James E. Knox                 
     -------------------------------
        James E. Knox (Attorney in fact)
James E. Knox, as attorney in fact for each person indicated





                                       6
<PAGE>   7
                                 EXHIBIT INDEX



Exhibit                                                           Sequentially
 Number                                 Exhibit                   Numbered Page
-------                                 -------                   -------------

  (4a)                  1998 Stock Incentive Plan


  (4b)                  Form of Stock Option Grant (incorporated
                        by reference from Anixter International
                        Inc.'s Annual Report on Form 10-K for
                        the fiscal year ended December 31, 1995,
                        Exhibit 10.27).


  (5)                   Opinion and Consent of James E. Knox, Esq.


  (23)                  Consent of Ernst & Young LLP.


  (24)                  Power of Attorney.



                                       7
[{"type": "S-8", "sequence": "1", "description": "FORM S-8", "secsgml_size_bytes": 16843}]
{"company-data": {"conformed-name": "ANIXTER INTERNATIONAL INC", "cik": "0000052795", "assigned-sic": "5063", "irs-number": "941658138", "state-of-incorporation": "DE", "fiscal-year-end": "1231"}, "filing-values": {"form-type": "S-8", "act": "33", "file-number": "333-56935", "film-number": "98648978"}, "business-address": {"street1": "4711 GOLF ROAD", "city": "SKOKIE", "state": "IL", "zip": "60076", "phone": "3129021515"}, "mail-address": {"street1": "4711 GOLF RD", "city": "SKOKIE", "state": "IL", "zip": "60076"}, "former-company": [{"former-conformed-name": "ITEL CORP", "date-changed": "19920703"}, {"former-conformed-name": "SSI COMPUTER", "date-changed": "19710316"}, {"former-conformed-name": "SSI COMPUTER CORP", "date-changed": "19690727"}]}
1
================================================================================
     As filed with the Securities and Exchange Commission on June 15, 1998
                                                                 File No. 33-

                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                           --------------------------
                                    FORM S-8
                             REGISTRATION STATEMENT
                                     Under
                           THE SECURITIES ACT OF 1933
                           --------------------------

                           Anixter International Inc.
             (Exact Name of Registrant as Specified in its Charter)

            Delaware                                     94-1658138
  (State or Other Jurisdiction              (I.R.S. Employer Identification No.)
of Incorporation or Organization)   

        4711 Golf Road
            Skokie, Illinois                               60076
(Address of Principal Executive Offices)                  (Zip Code)

                           ANIXTER INTERNATIONAL INC.
                           1998 Stock Incentive Plan
                            (Full Title of the Plan)

                                   John Dul
                                4711 Golf Road
                            Skokie, Illinois  60076
                    (Name and Address of Agent For Service)

                                 (847) 677-2600
         (Telephone Number, Including Area Code, of Agent For Service)

                        -------------------------------

                        CALCULATION OF REGISTRATION FEE
========================================================================================================================
                                       Amount               Proposed              Proposed Maximum          Amount of
       Title of Securities             to be            Maximum Offering         Aggregate Offering       Registration
         to be Registered            Registered        Price Per Share(1)             Price(1)                 Fee
------------------------------------------------------------------------------------------------------------------------
  Common Stock ($1.00 per             3,000,000           $18.125                   $54,375,000            $16,041
  share par value)............        shares              
========================================================================================================================
(1)  Estimated solely for the purpose of calculating the registration fee
     pursuant to Rule 457(h) on the basis of the average of the high and low
     prices as reported on the Composition Tape for the New York Stock Exchange
     on June 12, 1998.
2
                                    Part II

                            INFORMATION REQUIRED IN
                           THE REGISTRATION STATEMENT

ITEM 3.   INCORPORATION OF DOCUMENTS BY REFERENCE.

      The following documents, which have heretofore been filed by Anixter
International Inc., a Delaware corporation (the "Company"), with the Securities
and Exchange Commission (the "Commission") pursuant to the Securities Act of
1933, as amended (the "Securities Act"), and the Securities Exchange Act of
1934, as amended (the "Exchange Act"), are incorporated by reference herein and
shall be deemed to be a part hereof:

      (a) The Company's Annual Report on Form 10-K for the year ended 
          January 2, 1998.

      (b) The description of the Company's Common Stock under the caption
          "Description of Registrant's Securities to be Registered" included in
          the Company's Registration Statement No. 33-12390 dated March 4,
          1987.
        
      (c) The Company's Quarterly Report on Form 10-Q for the 13 weeks ended
          April 3, 1998.

      All documents subsequently filed by the Company pursuant to Section
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 herein by reference and shall be
deemed a part hereof from the date of filing of such documents.

ITEM 4.   DESCRIPTION OF SECURITIES.

      Not applicable.

ITEM 5.   INTERESTS OF NAMED EXPERTS AND COUNSEL.

      Certain Legal matters with respect to the legality of the Common Stock
offered hereby will be passed upon for the Company by James E. Knox, Senior
Vice President-Law and Secretary of the Company.  Mr. Knox holds a total of 
approximately 562,000 shares and options to acquire shares of Common Stock.

ITEM 6.   INDEMNIFICATION OF DIRECTORS AND OFFICERS.

      Section 145 of the Delaware General Corporation Law (the "DGCL") and
Article IX of the Company's By-laws authorize and empower the Company to
indemnify the directors, officers, employees and agents of the Company against
liabilities incurred in connection with, and related expenses resulting from,
any claim, action or suit brought against any such person as a result of his
relationship with the Company, provided that such persons acted in accordance
with a stated standard of conduct in connection with the acts or events on
which such claim, action or suit is

                                       2
3
based.  The finding of either civil or criminal liability on the part of such
persons in connection with such acts or events is not necessarily determinative
of the questions of whether such persons have met the required standard of
conduct and are, accordingly, entitled to be indemnified.

      In addition, Article IX of the Company's Restated Certificate of
Incorporation, as amended, provides that the Company's directors do not have
personal liability to the Company or its stockholders for monetary damages for
any breach of their fiduciary duty as directors except (i) for a breach of the
duty of loyalty, (ii) for acts or omissions not in good faith or which involve
intentional misconduct or knowing violation of the law, (iii) for willful or
negligent violations of certain provisions in the DGCL imposing certain
requirements with respect to stock repurchases, redemptions and dividends or
(iv) for any transaction from which the director derived an improper personal
benefit.  Subject to these exceptions, under Article IX directors do not have
any personal liability to the Company or its stockholders for any violation of
their fiduciary duty.

      The Company has entered into indemnification agreements with each of its
directors and officers (the "Indemnification Agreements").  The Indemnification
Agreements provide for the prompt indemnification "to the fullest extent
permitted by law" and for the prompt advancement of expenses, including
attorney's fees and other costs, expenses and obligations paid or incurred in
connection with investigating, defending, being a witness or participating in
(including on appeal) any threatened, pending or completed action, suit or
proceeding related to the fact that such director or officer is or was a
director, officer, employee, trustee, agent or fiduciary of the Company or is
or was serving at the request of the Company as a director, officer, employee,
trustee, agent or fiduciary of another corporation, partnership, joint venture,
employee benefit plan, trust or other enterprise, or by reason of anything done
by a director in any such capacity.  The Indemnification Agreements further
provide that the Company has the burden of providing that a director or officer
is not entitled to indemnification in any particular case.

      The Company has purchase insurance policies that, if any officer or
director of the Company or its subsidiaries becomes legally obligated to make a
payment (including legal fees and expenses) in connection with an alleged
wrongful act, the insurer will reimburse such officers and directors if the
indemnification payments, as provided above, are not made by the Company or its
subsidiaries to such officers and directors.  Wrongful act means any breach of
duty, neglect, error, misstatement, misleading statement or other act done by
an officer or director of the Company or any subsidiary.

ITEM 7.   EXEMPTION FROM REGISTRATION CLAIMED.

      Not applicable.

ITEM 8.   EXHIBITS.

      See Exhibit Index which is incorporated herein by reference.

                                       3
4
ITEM 9.   UNDERTAKINGS.

      The undersigned registrant hereby undertakes:

          1.      To file, during any period in which offers or sales are being
                  made, a post-effective amendment to this registration
                  statement:

                  (i)      To include any prospectus required by section
                           10(a)(3) of the Securities Act of 1933;

                  (ii)     To reflect in the prospectus any facts or events
                           arising after the effective date of the registration
                           statement (or the most recent post-effective
                           amendment thereof) which, individually or in the
                           aggregate, represent a fundamental change in the
                           information set forth in the registration statement;

                  (iii)    To include any material information with respect to
                           the plan of distribution not previously disclosed in
                           the registration statement or any material change to
                           such information in the registration statement;

                           Provided, however, that paragraphs (1)(i) and
                           (1)(ii) do not apply if the registration statement
                           is on Form S-3 or Form S-8, and the information
                           required to be included in a post- effective
                           amendment by those paragraphs is contained in
                           periodic reports filed by the registrant pursuant to
                           section 13 or section 15(d) of the Securities
                           Exchange Act of 1934 that are incorporated by
                           reference in the 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.

          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 the
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.

                                       4
5

      Pursuant to the requirements of the Securities Act of 1933, the
registrant certifies that it has duly caused this registration statement, or
amendment thereto, to be signed on its behalf by the undersigned, thereunto
duly authorized, in the City of Chicago, State of Illinois on June 12, 1998.

                        Anixter International Inc.
                   
                   
                            /s/       James E. Knox                    
                        -----------------------------------------------
                                      James E. Knox
                         Senior Vice President-Law and Secretary

     PURSUANT TO THE REQUIREMENTS OF THE SECURITIES EXCHANGE ACT OF 1933, THIS
REGISTRATION STATEMENT HAS BEEN SIGNED BELOW ON JUNE 10, 1996 BY THE FOLLOWING
PERSONS ON BEHALF OF THE REGISTRANT IN THE CAPACITIES INDICATED.

               LORD JAMES BLYTH*                        Director
---------------------------------------                         
               Lord James Blyth          
                                         
               ROD F. DAMMEYER*                         Director               
---------------------------------------                                        
               Rod F. Dammeyer                        
                                         
               ROBERT E. FOWLER, JR.*                   Director  
---------------------------------------                         
               Robert E. Fowler, Jr.     
                                         
     /s/       JAMES M. FROISLAND               Vice President-Controller
---------------------------------------                                  
               James M. Froisland        
                                         
     /s/       ROBERT W. GRUBBS            President, Chief Executive Officer, 
---------------------------------------               and Director             
               Robert W. Grubbs          
                                         
               F. PHILIP HANDY*                         Director
----------------------------------------                        
               F. Philip Handy           
                                         
               MELVYN N. KLEIN*                         Director
----------------------------------------                        
               Melvyn N. Klein           
                                         
   /s/         DENNIS J. LETHAM                Sr. Vice President-Finance and
---------------------------------------            Chief Financial Officer
               Dennis J. Letham                  
                                         
                JOHN R. PETTY*                          Director
---------------------------------------                         
                John R. Petty            
                                         
               SHELI Z. ROSENBERG*                      Director
---------------------------------------                         
              Sheli Z. Rosenberg              

                                       5
6
          STUART M. SLOAN*                    Director
----------------------------------------              
          Stuart M. Sloan               
                                        
          THOMAS C. THEOBALD*                 Director
----------------------------------------              
          Thomas C. Theobald            
                                        
          SAM ZELL*                           Director
----------------------------------------              
          Sam Zell                      
                                        

*By        /s/    James E. Knox                 
     -------------------------------
        James E. Knox (Attorney in fact)
James E. Knox, as attorney in fact for each person indicated

                                       6
7
                                 EXHIBIT INDEX

Exhibit                                                           Sequentially
 Number                                 Exhibit                   Numbered Page
-------                                 -------                   -------------

  (4a)                  1998 Stock Incentive Plan

  (4b)                  Form of Stock Option Grant (incorporated
                        by reference from Anixter International
                        Inc.'s Annual Report on Form 10-K for
                        the fiscal year ended December 31, 1995,
                        Exhibit 10.27).

  (5)                   Opinion and Consent of James E. Knox, Esq.

  (23)                  Consent of Ernst & Young LLP.

  (24)                  Power of Attorney.

                                       7