FIRST TRUST PORTFOLIOS L.P. 120 EAST LIBERTY DRIVE WHEATON, ILLINOIS 60187 December 7, 2022 Securities and Exchange Commission 100 F Street NE Washington D.C. 20549 Attn: Filing Desk, Stop 1-4 Re: FT 10429 (File No. 333-267877) (CIK No. 1942626) Gentlemen: In accordance with the provisions of Rule 497(j) of Regulation C under the Securities Act of 1933 (the "Securities Act") this letter serves to certify that the most recent amendment to the registration statement on Form S-6 for the above captioned Trust does not differ from that which would have been filed pursuant to Rule 497(b) of the Securities Act. Amendment No. 1, which was the most recent Amendment to the Registration Statement, was filed electronically with the Commission on December 5, 2022. Very truly yours, FT 10429, Registrant /s/ First Trust Portfolios L.P. By: FIRST TRUST PORTFOLIOS L.P., Depositor