Abstract: A web winding machine includes two roll beds each formed of two roll support rollers. Each bed receives a respective web roll being wound thereon. The web rolls are at separate locations across the width of the machine. For at least one roll bed, a longitudinally extending packing is introduced from below into the gap between the two support rollers of the bed. A respective movable packing element is at the end of each wound roll and forms a packing gap with the wound roll and with the wall surfaces of the support rollers to enclose a pressure space. A compressed air cushion can be built up below the wound roll in the bed. At least one of the rollers of the roll bed has a perforated roller shell. A stationary pressure chamber inside the shell delivers pressure through the shell into the pressure space. The pressure chamber in the shell can be divided into sections along the axis of the roller. The pressure chamber is adapted to be connected to a source of compressed air.