Analytical and numerical results for fixed-end torsion of cylindrical specimen are presented. Finite-strain elastoplastic kinematics based on multiplicative split of deformation gradient tensor is adopted. The constitutive relations are a combination of an arbitrary hyperelastic model based on the first invariant of the left Cauchy–Green deformation tensor and the J2–plasticity model with an arbitrary isotropic strain hardening. The integral characteristics of the process, namely, torque and axial force (Swift effect), are compared with the known exact solution for a neo-Hookean hyperelastic material with Tresca yield condition. The axial force predicted by these models can differ markedly, but the torque is almost the same. For the materials with yield stress saturation, we find the limit in torque and axial force.