The invention relates to a plunger (1) for a fuel injection pump, having a tube-like housing (2), which accommodates a roller (4) for the running of a periodic lift generator inside the inner jacket (5) thereof in the region of a first ring end (3). Said roller has axial stumps (7) projecting from the end faces (6) of the roller, by means of 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 jacket (5) of the housing (2), proceeding from the first ring end thereof in the direction of the second rind end (3, 10) and at least in the circumferential section (13) thereof, which surrounds an outer jacket (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.