A stacker apparatus for flat sheet material has a suction drum rotating on a stator. The suction drum grips the flat sheet material at one tangential position, arcuately moves it, and releases it on a stack at a second tangential position. The suction drum has a section containing a plurality of suction openings for gripping the sheet material. A plurality of peripheral suction channels on the stator communicate with the suction openings. The width of the suction channels decreases step-wise along their length so that the suction openings are initially in full communication with the channels, thereafter the suction openings are partially closed, and finally, selected ones of the suction openings are completely closed as the drum rotates.