An apparatus includes a crimping device for producing individual, pillow-shaped, preferably filled, hollow bodies from plastically deformable tubes separated transversely to their longitudinal direction and delimited at opposite ends by crimped edges. The crimping device has at least one elongate crimping unit assigned to the longitudinal direction of the tubes, on which a row of crimping tools is disposed one behind the other in the longitudinal direction. Each crimping tool has a stationary crimping jaw fixed in the frame and a movable crimping jaw lying opposite to the fixed jaw in the transverse direction and disposed on a carriage movable back and forth in the transverse direction in the frame. All of the movable crimping jaws may be fastened on the carriage to actuate all of the crimping tools simultaneously and thereby separate a tube into a number of hollow bodies.