There is described a sheet-fed stamping press (10*) comprising a foil application unit (2*) designed to allow transfer or lamination of foil material onto successive sheets (S), which foil material is fed to the foil application unit (2*) in the form of a foil carrier (FC) supplied by means of a foil feeding system (3). The foil application unit (2*) comprises a stamping cylinder (21) at least one circumferential stamping section (210) provided on a circumference of the stamping cylinder (21) and comprising successive stamping segments (211 *; 211 **) distributed one after the other about the circumference of the stamping cylinder (21), the stamping cylinder (21) also acting as sheet-transporting cylinder and comprising multiple sheet holding units (21a) distributed about the circumference of the stamping cylinder (21) and designed to hold successive sheets (S) against the circumference of the stamping cylinder (21). The foil application unit (2*) further comprises a plurality of counter-pressure units (25) distributed about a portion of the circumference of the stamping cylinder (21) and designed to press the successive sheets (S) and the foil carrier (FC) against an outer surface of the stamping segments (211 *; 211 **), the foil carrier (FC) being supplied by the foil feeding system (3) between the sheets (S) and the stamping segments (211 *; 211 **). Each counter-pressure unit (25) is designed as a cylinder unit (250, 255) provided with at least one circumferential pressing element (255) positioned to cooperate with the circumferential stamping section (210) of the stamping cylinder