A device for printing hollow bodies includes a rubber blanket cylinder. A supply device, which guides the hollow bodies to the rubber blanket cylinder, is provided. The supply device comprises a mandrel which is rotated by a drive. One of the hollow bodies to be printed is arranged coaxially on the mandrel. An axial spacing between the mandrel and the rubber blanket cylinder can be changed as a result of an adjusting movement of the supply device. The adjusting movement of the supply device is a linear adjusting movement. The supply device is configured as a linear system which radially supplies the hollow bodies to the rubber blanket cylinder individually and one after the other. The supply device has multiple different positions, each of which places the respective hollow body to be printed, along the adjustment path of the supply device. The positions are arranged at different respective radial distances with respect to the rubber blanket cylinder.