<PAGE>   1

                                                                   EXHIBIT 4.13


                          FIRST SUPPLEMENTAL INDENTURE

THIS FIRST SUPPLEMENTAL INDENTURE, dated as of January 20, 2000, is executed by
METAL MANAGEMENT SERVICES, INC., a Delaware corporation ("Services"), METAL
MANAGEMENT STAINLESS & ALLOY, INC., a Delaware corporation ("S&A"), and METAL
MANAGEMENT WEST COAST HOLDINGS, INC., a Delaware corporation ("Holdings"), each
a wholly-owned subsidiary of METAL MANAGEMENT, INC., a Delaware corporation (the
"Company"), for the sole purpose of granting a guarantee under the Indenture (as
amended from time to time, the "Indenture"), dated as of May 7, 1999, with
respect to the Company's 12 3/4% Senior Secured Notes due 2004 (the "Notes"),
entered into among the Company, the Guarantors (as defined therein) and HARRIS
TRUST AND SAVINGS BANK, as trustee (the "Trustee").

                              PRELIMINARY STATEMENT

The Company, the Guarantors and the Trustee have entered into the Indenture.
Capitalized terms used herein, not otherwise defined herein, shall have the
meanings given them in the Indenture.

Section 4.18 of the Indenture expressly provides that any Restricted Subsidiary
(i) that has assets or revenues in any fiscal year in excess of $200,000, (ii)
that, together with all other Restricted Subsidiaries that are not Guarantors,
has assets or revenues in any fiscal year in excess of $1.0 million in the
aggregate, or (iii) that is not a Guarantor and guarantees any Indebtedness of
the Company, other than the Notes, or is a borrower under the Senior Credit
Facility, shall execute a supplemental indenture to become a Guarantor of the
Company's Notes. Pursuant to Section 4.18 of the Indenture, each of Services,
S&A and Holdings execute this First Supplemental Indenture to a become Guarantor
of the Company's Notes. Each of Services, S&A and Holdings have, by Board
Resolution, authorized this First Supplemental Indenture. The Trustee has
determined that this First Supplemental Indenture is in form satisfactory to it.

NOW, THEREFORE, it is mutually covenanted and agreed, for the equal and
proportionate benefit of all Holders of the Notes issued under the Indenture
from and after the date of this First Supplemental Indenture, as follows:

     Section 1.

     Guarantee on the Notes.
     -----------------------



<PAGE>   2


Each of Services, S&A and Holdings hereby subjects itself to the provisions of
the Indenture as a Guarantor in accordance with Article 10 of the Indenture.

     Section 2.

     Counterparts
     ------------

This First Supplemental Indenture may be executed in several counterparts, all
of which together shall constitute one agreement binding on all parties,
notwithstanding that all parties have not signed the same counterpart.





<PAGE>   3



IN WITNESS WHEREOF, the undersigned have caused this First Supplemental
Indenture to be duly executed by its respective officers as of the day and year
first above written.

                           METAL MANAGEMENT SERVICES, INC.
                           METAL MANAGEMENT STAINLESS &
                                    ALLOY, INC.
                           METAL MANAGEMENT WEST COAST
                                    HOLDINGS, INC.


                           By: /s/ David A. Carpenter
                               -----------------------------------------
                           Name: David A. Carpenter
                           Its:  Vice President