A tappet (1) for a fuel injection pump, having a tube-like housing (2), which accommodates a roller (4) for the running on a periodic lift generator inside the inner lateral surface (5) thereof in the region of a first ring end (3). This roller has axle stumps (7) projecting from the end faces (6) of the roller, by which stumps the roller sits in recesses (8) in the housing (2), wherein the housing (2) is penetrated axially by a bridge piece (9) underneath the roller (4), the underside (11) of which bridge piece, which faces a second ring end (10) of the housing (2), acts as a rest for a plunger following part. The inner lateral surface (5) of the housing (2), proceeding from the first ring end thereof in the direction of the second ring end (3, 10) and at least in the circumferential section (13) thereof, which surrounds an outer lateral surface (12) of the roller (4), has a pocket-like thinned portion of material (14), which levels out under a half of the height of the roller (4) and into which the ring edges (15) of the roller (4) project.