Abstract: A cradle-type winding machine has a pair of driven rollers receiving the sleeves on which the web is to be wound in a winding bed and a weakening device perforating the web upon temporary halting of the latter. A support can be raised into the winding bed and carries both a clamping roller and a swingable blade, the former being effective to clamp the web against one of the support rollers for the winding of heavy paper stack while the latter can be swung into a position enabling the tearing of light paper stack. When heavy paper stack is used, a perforator along the path of the web before it encounters the support rollers against which it is to lie is provided to perforate the web across its width and form a weakened zone on opposite sides of which adhesive strips are provided.