File No. 33-27172

811-05719

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM N-1A

REGISTRATION STATEMENT UNDER THE SECURITIES ACT OF 1933[X]

Pre-Effective Amendment No.[__]

Post-Effective Amendment No. 48[X]

and/or

REGISTRATION STATEMENT UNDER THE INVESTMENT COMPANY ACT OF 1940[X]

Amendment No. 48[X]

(Check appropriate box or boxes.)

BNY Mellon Stock Index Fund, Inc.

(Exact Name of Registrant as Specified in Charter)

c/o BNY Mellon Investment Adviser, Inc.

240 Greenwich Street, New York, New York 10286

(Address of Principal Executive Offices) (Zip Code)

Registrant's Telephone Number, including Area Code: (212) 922-6400

Bennett A. MacDougall, Esq.

240 Greenwich Street

New York, New York 10286

(Name and Address of Agent for Service)

It is proposed that this filing will become effective (check appropriate box)

X__ immediately upon filing pursuant to paragraph (b)

_____on (date) pursuant to paragraph (b)

_____ (days) days after filing pursuant to paragraph (a)(1)

_____on (date) pursuant to paragraph (a)(1)

_____ (days) days after filing pursuant to paragraph (a)(2)

_____on (date) pursuant to paragraph (a)(2) of Rule 485

If appropriate, check the following box:

_____this post-effective amendment designates a new effective date for a previously filed post-effective amendment.

SIGNATURES

Pursuant to the requirements of the Securities Act of 1933 and the Investment Company Act of 1940, the Registrant certifies that it meets all of the requirements for effectiveness of this Amendment to the Registration Statement pursuant to Rule 485(b) under the Securities Act of 1933 and has duly caused this Amendment to the Registration Statement to be signed on its behalf by the undersigned, duly authorized, in the City of New York, and State of New York on the 8th day of May 2020.

BNY Mellon Stock Index Fund, Inc.

BY:	/s/ Renee LaRoche-Morris*
	Renee LaRoche-Morris, PRESIDENT

Pursuant to the requirements of the Securities Act of 1933, this Amendment to the Registration Statement has been signed below by the following persons in the capacities and on the date indicated.

Signatures	Title	Date
/s/ Renee LaRoche-Morris*	President (Principal Executive Officer)	5/8/2020
Renee LaRoche-Morris
/s/ James Windels*	Treasurer (Principal Financial	5/8/2020
James Windels	and Accounting Officer)
/s/ Joseph S. DiMartino*	Chairman of the Board	5/8/2020
Joseph S. DiMartino
/s/ Peggy C. Davis*	Board Member	5/8/2020
Peggy C. Davis
/s/ Gina D. France*	Board Member	5/8/2020

Gina D. France
/s/ Joan L. Gulley*		Board Member	5/8/2020
Joan L. Gulley
/s/ Ehud Houminer*		Board Member	5/8/2020
Ehud Houminer
/s/ Robin A. Melvin*		Board Member	5/8/2020
Robin A. Melvin
*BY:	/s/ Sonalee Cross
	Sonalee Cross Attorney-in-Fact

INDEX OF EXHIBITS

Exhibits

EX-101.INS – Instance Document.

EX-101.SCH – Taxonomy.

EX-101.CAL – Calculation Linkbase.

EX-101.DEF – Definition Linkbase.

EX-101.LAB – Labels Linkbase.

EX-101.PRE – Presentation Linkbase.