Analytical solutions are obtained for elastic-plastic deformations of a linearly hardening rotating solid shaft with fixed ends and with free ends. All stages of elastic-plastic deformations are studied using Tresca's yield condition and the flow rule associated with it. Expressions for the stresses, displacement and plastic strains for a perfectly plastic shaft can be deduced from the expressions of linearly hardening shaft by letting the hardening parameter vanish. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.