A mechanical tappet (101, 201, 301, 401, 501, 601, 701, 801, 901, 1001) is provided, in particular for actuating the lifting of a pump piston (39) of a fuel pump of an internal combustion engine, with a sleeve-shaped tappet housing (102, 202, 302, 402, 502, 602, 702, 902, 1002) constructed as a shaped sheet-metal part and with a driving roller (6) supported so that it can rotate. Here, a bolt (4) supports the driving roller so that it is centered, and end sections (7) of the bolt projecting from the driving roller are supported in bolt eyes (8) of the tappet housing.