September 14, 2020

BNY MELLON STOCK INDEX FUND, INC.

Supplement to Current Summary Prospectus and Prospectus

Effective October 26, 2020, the following information will supersede and replace the information contained in the sections "Portfolio Management" in the summary prospectus and "Fund Summary – Portfolio Management" in the prospectus:

The fund's investment adviser is BNY Mellon Investment Adviser, Inc. (BNYM Investment Adviser). BNYM Investment Adviser has engaged its affiliate, Mellon Investments Corporation (Mellon), to serve as the fund's index manager. 

Thomas J. Durante, CFA, David France, CFA, Todd Frysinger, CFA, Vlasta Sheremeta, CFA, Michael Stoll and Marlene Walker Smith are the fund's primary portfolio managers.  Mr. Durante has been a primary portfolio manager of the fund since March 2000 and Messrs. France, Frysinger and Stoll and Mses. Walker Smith and Sheremeta have been primary portfolio managers of the fund since October 2020.  Mr. Durante is a managing director and co-head of equity index portfolio management at Mellon.  Messrs. France, Frysinger and Stoll and Ms. Sheremeta are each a vice president and senior portfolio manager at Mellon. Ms. Walker Smith is a director and co-head of equity index portfolio management at Mellon.  

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Effective October 26, 2020, the following information will supersede and replace the fourth paragraph in the section "Fund Details – Management" in the prospectus:

Thomas J. Durante, CFA, David France, CFA, Todd Frysinger, CFA, Vlasta Sheremeta, CFA, Michael Stoll and Marlene Walker Smith are the fund's primary portfolio managers.  Messrs. Durante, France, Frysinger and Stoll and Mses. Sheremeta and Walker Smith are employees of Mellon Investments Corporation and are jointly and primarily responsible for managing the fund's portfolio.  Mr. Durante has been a primary portfolio manager of the fund since March 2000 and Messrs. France, Frysinger and Stoll and Mses. Walker Smith and Sheremeta have been primary portfolio managers of the fund since October 2020.  Mr. Durante is a managing director and co-head of equity index portfolio management at Mellon.  He has been employed by Mellon or a predecessor company since 2000.  Mr. France is a vice president and senior portfolio manager at Mellon.  He has been employed by Mellon or a predecessor company since 2009.  Mr. Frysinger is a vice president and senior portfolio manager at Mellon.  He has been employed by Mellon or a predecessor company since 2007.  Ms. Sheremeta is a vice president and senior portfolio manager at Mellon.  She has been employed by Mellon or a predecessor company since 2011.  Mr. Stoll is a vice president and senior portfolio manager at Mellon.  He has been employed by Mellon or a predecessor company since 2005.  Ms. Walker Smith is a director and co-head of equity index portfolio management at Mellon.  She has been employed by Mellon or a predecessor company since 1995,

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