<p>The main purpose of the presented study is to evaluate the impact of the intermediate principal stress effect on the elastoplastic response of a rotating cylinder. To this end, new closed-form analytical solutions in the framework of infinitesimal strains are presented for the displacement, stresses and plastic strains in the rotating solid and hollow cylinders with fixed and free ends. The analysis is based on the unified yield criterion (UYC), the flow rule associated with it and the law of linear isotropic hardening. Only the loading stage is considered. The exact solutions for all possible plastic regimes of the UYC are obtained in the unified manner. Purely plastic and fully plastic stress states are studied in detail. Special attention is paid to the calculation of the plastic limit angular velocity depending on mechanical and geometrical parameters of a cylinder. The traditional solutions based on Tresca and Schmidt-Ishlinsky yield criteria are special cases of the found unified solution. The novelty of the present study is to present an exact analytical solution including the effect of the intermediate principal stress. It is established that the elastoplastic response of the rotating cylinder and plastic limit angular velocity are considerably impacted by the intermediate principal stress effect. The obtained results are compared with solutions available in the literature for appropriate values of the mechanical parameters and good agreement is observed. The presented unified solution can be used to predict the stress response and the plastic limit angular velocity of the rotating cylinders for all kinds of isotropic linear hardening materials without strength differential effect.</p>