To prevent lowering of nip pressure in the vicinity of a shaft end while preventing the generation of damage in a rubber material on the outer periphery of a core material in a roller for an offset press suitable for use in the water fountain roller to be provided in the damping arrangement of the printing apparatus of the offset press.

The roller 22 for the offset press is provided in the printing apparatus of the offset press with the rubber material 6 coming into contact with a partner roller 23 under pressure to generate nip pressure in the outer periphery of the core material. Flanges 5 have an outer diameter (d) slightly smaller than the outer diameter D of the roller, regulate the movement of the rubber material 6 to the outside in the axial direction of the roller, and are provided at both ends in the axial direction of the roller so as to be paired.