The invention proposes an apparatus for stacking individual sheets, having a frame (1, 2, 3), a support element (4) which can be displaceably guided on the frame and has an abutment surface for the stack of individual sheets, and having a pressing roll (5) for alternately displacing and releasing the support element (4). The pressing roll (5) comprises a pressing shaft (16) which is rotatably mounted on the frame (1, 2, 3), two pressing roll side parts (17, 18) which are fixed to the pressing shaft, and at least two sliding shafts (19) which are rotatably or fixedly arranged on the pressing roll side parts and have rotatably or fixedly arranged sliding rollers (20). A drive is provided for the purpose of rotating the pressing roll.