Abstract: To effectively counteract any deformation of the pressing roller of a rubber blanket cleaning device for offset printing machines, a cleaning blanket is passed over the pressing roller and a blanket is brought into contact with the rubber cylinder. To improve the cleaning process, a pressing roller support is arranged at the periphery of the pressing roller, whose outer contour can, in non-loaded state, pass by the roller-side surface of the pressing roller support free from pressure and play. The pressing roller support is positioned parallel to the axis of the pressing roller and approximately diametrically opposite to the arc region, while coming into contact with the pressing roller of the rubber cylinder.