Provided is a tire building drum and a method for shaping tire components on the tire building drum, wherein the tire building drum has an annular sleeve that extends over turn-up arms in the longitudinal direction of the turn-up arms. The sleeve is elastic in the circumferential direction and fits elastically around the turn-up arms. The sleeve is provided with inelastic reinforcement elements extending in at least a part of the sleeve in a reinforcement direction transverse to the circumferential direction of the tire building drum, and has a fixed end that is retained in the axial direction and a movable end that is movable over the turn-up arms in their respective longitudinal directions.