The article is devoted to the elastic-plastic analysis of a rotating hollow cylinder with fixed ends. It is assumed that the strains in a cylinder are infinitesimal and additively decomposed into elastic and plastic components. The elastic component of strain is determined in accordance with Hooke's law. The Tresca’s yield condition, the flow rule associated with it and the power law of hardening are adopted in order to calculate plastic strains. The presented analysis covers both loading and unloading stages. Unloading of a cylinder is assumed to be purely elastic. For a number of special cases of the hardening law, an analytical solution of the formulated system of equations is found. Special attention is paid to the calculation of the angular velocity corresponding to the complete transition of a cylinder to the plastic state. Dependencies of the fully-plastic limit angular velocity on the hardening parameters are established.