<PAGE>   1
 
     AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON JULY 16, 1998
 
                                                     REGISTRATION NO. 333-
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                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
                            ------------------------
 
                                    FORM S-4
                             REGISTRATION STATEMENT
                                     UNDER
                      THE SECURITIES EXCHANGE ACT OF 1933
 
                         ALLIED WASTE INDUSTRIES, INC.
               (EXACT NAME OF REGISTRANT AS SPECIFIED IN CHARTER)
 
<TABLE>
<S>                                  <C>                                  <C>
              DELAWARE                               4953                              88-0228636
    (STATE OR OTHER JURISDICTION         (PRIMARY STANDARD INDUSTRIAL               (I.R.S. EMPLOYER
 OF INCORPORATION OR ORGANIZATION)       CLASSIFICATION CODE NUMBER)             IDENTIFICATION NUMBER)
</TABLE>
 
                    15880 N. GREENWAY-HAYDEN LOOP, SUITE 100
                           SCOTTSDALE, ARIZONA 85260
                                 (602) 423-2946
  (ADDRESS, INCLUDING ZIP CODE, AND TELEPHONE NUMBER, INCLUDING AREA CODE, OF
                   REGISTRANT'S PRINCIPAL EXECUTIVE OFFICES)
                            ------------------------
 
                                 STEVEN M. HELM
                             VICE PRESIDENT--LEGAL
                            AND CORPORATE SECRETARY
                         ALLIED WASTE INDUSTRIES, INC.
                  15880 NORTH GREENWAY-HAYDEN LOOP, SUITE 100
                           SCOTTSDALE, ARIZONA 85260
                                 (602) 423-2946
 
                                WITH COPIES TO:
 
                                 DAVID C. GOLAY
                    FRIED, FRANK, HARRIS, SHRIVER & JACOBSON
                               ONE NEW YORK PLAZA
                            NEW YORK, NEW YORK 10004
                                 (212) 859-8000
                            ------------------------
 
     APPROXIMATE DATE OF COMMENCEMENT OF PROPOSED SALE TO THE PUBLIC: As soon as
practicable after this Registration Statement becomes effective.
 
     If any of the securities being registered on this form are to be offered in
connection with the termination of a holding company and there is compliance
with General Instruction G, check the following box  [ ].
 
     If this form is filed to register additional securities for an offering
pursuant to Rule 462(b) under the Securities Act, check the following box and
list the Securities Act registration statement number of the earlier effective
registration statement for the same offering  [X]. 333-52501
 
     If this form is a post-effective amendment filed pursuant to Rule 462(d)
under the Securities Act, check the following box and list the Securities Act
registration statement number of the earlier effective registration statement
for the same offering  [ ].
                            ------------------------
 
                        CALCULATION OF REGISTRATION FEE
 
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<CAPTION>
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                                                                    PROPOSED MAXIMUM     PROPOSED MAXIMUM
           TITLE OF EACH CLASS OF                 AMOUNT TO        OFFERING PRICE PER   AGGREGATE OFFERING       AMOUNT OF
        SECURITIES TO BE REGISTERED            BE REGISTERED(1)         SHARE(1)             PRICE(1)       REGISTRATION FEE(1)
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<S>                                          <C>                  <C>                  <C>                  <C>
Common Stock, par value $.01 per share......      1,956,665            $26.53125           $51,912,768            $15,315
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(1) Pursuant to Rule 457(c), National Market tier of the registration fee is
    calculated based on the average of the high and low prices for the Common
    Stock, as reported on the National Market tier of the Nasdaq Stock Market
    Inc. on July 10, 1998.
 
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<PAGE>   2
                                Explanatory Note


     This registration statement is being filed pursuant to Rule 462(b) under
the Securities Act of 1933, as amended ("Rule 462(b)"), and includes the
registration statement facing page, this explanatory note, a legal opinion and
an accountant's consent, which are filed as exhibits hereto, an exhibit index
and the signature page. Pursuant to Rule 462(b), the contents of the
registration statement on Form S-4 (File No. 333-52501) of Allied Waste
Industries, Inc., including the exhibits thereto, are incorporated by reference
into this registration statement.
<PAGE>   3
 
                                   SIGNATURES
 
     Pursuant to the requirements of the Securities Act of 1933, the Registrant
has duly caused this Registration Statement to be signed on its behalf by the
undersigned, thereunto duly authorized, in the City of Scottsdale, State of
Arizona, on July 16, 1998.
 
                                          ALLIED WASTE INDUSTRIES, INC.
 
                                          By:     /s/ HENRY L. HIRVELA
                                            ------------------------------------
                                                      Henry L. Hirvela
                                             Vice President -- Chief Financial
                                                           Officer
 
                               POWER OF ATTORNEY
 
     Each of the undersigned hereby appoints Thomas H. Van Weelden, Henry L.
Hirvela, James S. Eng, and each of them, with full power to act alone, as
attorney and agents for the undersigned, with full power of substitution, for
and in the name place and stead of the undersigned, to sign and file with the
Securities and Exchange Commission under the Securities Act of 1933 any and all
amendments and exhibits to this Registration Statement and any and all
applications, instruments and other documents to be filed with the Securities
and Exchange Commission pertaining to the registration of the securities covered
hereby, with full power and authority to do and perform any and all acts and
things whatsoever requisite or desirable.
 
     Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed by the following persons and in the
capacities indicated on July 16, 1998.
 
<TABLE>
<CAPTION>
                      SIGNATURE                                              TITLE
                      ---------                                              -----
<C>                                                      <S>
 
                 /s/ ROGER A. RAMSEY                     Chairman of the Board of Directors
-----------------------------------------------------
                   Roger A. Ramsey
 
              /s/ THOMAS H. VAN WEELDEN                  Director, President and Chief Executive
-----------------------------------------------------      Officer
                Thomas H. Van Weelden                      (Principal Executive Officer)
 
                /s/ HENRY L. HIRVELA                     Vice President -- Chief Financial Officer
-----------------------------------------------------      (Principal Financial Officer)
                  Henry L. Hirvela
 
                  /s/ JAMES S. ENG                       Corporate Controller
-----------------------------------------------------      (Principal Accounting Officer)
                    James S. Eng
 
                  /s/ NOLAN LEHMANN                      Director
-----------------------------------------------------
                    Nolan Lehmann
 
                 /s/ ALAN B. SHEPARD                     Director
-----------------------------------------------------
                   Alan B. Shepard
 
                /s/ DAVID B. KAPLAN                      Director
-----------------------------------------------------
                   David B. Kaplan
 
                  /s/ MICHAEL GROSS                      Director
-----------------------------------------------------
                    Michael Gross
</TABLE>
 
                                        2
<PAGE>   4
 
<TABLE>
<CAPTION>
                      SIGNATURE                                              TITLE
                      ---------                                              -----
<C>                                                      <S>
                /s/ ANTONY P. RESSLER                    Director
-----------------------------------------------------
                  Antony P. Ressler
 
                /s/ HOWARD A. LIPSON                     Director
-----------------------------------------------------
                  Howard A. Lipson
 
                 /s/ DENNIS HENDRIX                      Director
-----------------------------------------------------
                   Dennis Hendrix
 
                /s/ WARREN B. RUDMAN                     Director
-----------------------------------------------------
                  Warren B. Rudman
 
                  /s/ VINCENT TESE                       Director
-----------------------------------------------------
                    Vincent Tese
</TABLE>
<PAGE>   5
 
                                 EXHIBIT INDEX
 
<TABLE>
<CAPTION>
  EXHIBIT
    NO.                                      EXHIBIT
-----------                                  -------
<C>           <C>  <S>
    5.1       --   Opinion of Fried, Frank, Harris, Shriver & Jacobson, counsel
                   to Allied, as to the legality of the common stock being
                   offered.
   23.1       --   Consent of Arthur Andersen LLP.
   23.2       --   Consent of Fried, Frank, Harris, Shriver & Jacobson
                   (included in its opinion filed as Exhibit 5.1 hereto).
   24         --   Power of Attorney (included on the signature page to the
                   originally filed Registration Statement).
</TABLE>