The invention relates to a sleeve for mounting on carrier cylinders of printing machines, with two flange rings 11, 12 on the ends, on which a cylindrical outer sleeve wall 20 and an inner sleeve wall 30 are supported at a distance from each other. In order to create a sleeve, more particularly an adapter sleeve, that can be easily mounted on and removed from carrier cylinders, is cost-effective to produce, and with a comparatively low weight allows extremely high printing qualities, it is envisaged in accordance with the invention that the external sleeve wall 20 comprises a fibre composite material with at least one layer of a carbon fibres-nonwoven sheet 21 and that between the two flange rings 11, 12 at least one support ring 40, 40A is provided that supports the outer sleeve wall 20, vis-à-vis the inner sleeve wall 30.