May 25, 2021

BNY MELLON STOCK INDEX FUND, INC.

Supplement to Current Summary Prospectus and Prospectus

Effective June 30, 2021, 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.

David France, CFA, Todd Frysinger, CFA, Vlasta Sheremeta, CFA, Michael Stoll and Marlene Walker Smith are the fund's primary portfolio managers, positions they have held since October 2020. 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 head of equity index portfolio management at Mellon.

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Effective June 30, 2021, the following information will supersede and replace the fourth paragraph in the section "Fund Details – Management" in the prospectus:

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