Abstract: A machine for winding up rolls of piles of a sheet material or of bags made of plastics, comprising at least a plane on which piles of sheets are successively collected, at least a frame supporting a revolving body on which a pliers unit is mounted adapted to grip each sheet pile and to cause its rotation under the control of a motor so as to form a sheet roll, said frame being slidably mounted on a transverse guiding means and being actuated by a cylinder-piston unit designed to adjust the position of the frame carrying the pliers with regard of the sheet pile; a device being further provided for causing the controlled starting and stopping of said revolving body in a preestablished position, said device comprising a lever pivotally mounted about a pin and actuated by a cylinder-piston unit so as to let the free end of said lever to be engaged into a notch provided on the peripheral surface of the revolving body.