A device for stacking sheets comprises several disks arranged adjacent to each other on a driving shaft, the disks having spiral slots running from the outside towards the inside. The spiral slots of the disks overlap in an axial direction and together form a pocket into which the sheets conveyed. In order to guarantee trouble-free stacking of the sheets, the spiral slots of adjacent disks are staggered at least in the inner area of the stacker. Therefore, almost all the kinetic energy of a sheet which is inserted into the shot is issipated by frictional and flexing. The spiral slots of one or more disks may additionally be provided with elastic boundary walls.