Subject of the investigation is the deformation of a perfectly plastic cylinder with uniform temperature inside its cylindrical core and zero surface temperature. The calculation is based on Tresca's yield condition and the flow rule associated to it. For small radii of the hot core. a plastic region appears at the center and expands towards the surface of the cylinder with increasing core temperature. The other possibility is that, depending on the core radius, two plastic regions form one after the other or simultaneously, in the core and at the surface and join in the fully plastic state. The image points of the cylinder lie on different edges and sides of the Tresca-prism in stress space.