There is provided a coiling machine for coiling a continuous paper web having two large rolls that form a coil bed for uptake of a paper coil. The space bounded by the large rolls and the coil is formed as a pressure-tight chamber that has a compressed air connection. Particularly for the present invention, one of the two large rolls has a jacket that is essentially more intensely deformable than the jacket of the other roll and, thus, one large roll is softer than the other large roll. The upper vertex of the softer large roll is located lower than the upper vertex of the harder large roll. The web guidance is configured for one embodiment of the coiling machine such that the web is introduced from below, and between the two large rolls, to wind around the softer large roll. For another embodiment of the coiling machine, the web is introduced through a pressing gap between one of the large rolls and the coil.