A device for unstacking flat objects comprises an unstacking head (2) provided with a suction cup (88) for grasping the first flat object in a stack of such objects presented thereto and for moving a grasped flat object towards an exit position (40) in which the object is released. The suction cup (88) is a bellows suction cup made of a flexible material such that when it grasps the first flat object in the stack, it retracts under the effect of the suction and entrains at least the surface of the grasped object therewith as it retracts. A shoe (90) having a surface close to the grasping plane of the suction cup is disposed adjacent to the suction cup in fixed relationship relative to the mount (50) carrying the suction cup. The shoe thus constitutes an obstacle to the surface of a grasped flat object, thereby warping said surface as the suction cup retracts.