Summary: Large elastic-plastic torsion of uniform circular bars is investigated numerically, using special finite elements. Two end conditions corresponding to fixed-end torsion and free-end torsion, resp., are considered, taking full account of the axial effects. The analysis is carried out using an isotropic hardening as well as a recently proposed large deformation kinematic hardening model. Either linear hardening or power law hardening uniaxial stress-strain curves are assumed in the analysis [see E. Van der Giessen, Eur. J. Mech. A8, No.1, 15-34 (1989; Zbl 0665.73032)]. Results are presented in terms of predicted torque vs. twist curves for all cases. Furthermore, we present axial force vs. twist curves for fixed-end torsion or elongation vs. twist curves for free-end torsion. Special attention is paid to the so-called plastic spin, a concept which has recently been identified to play a key role in the description of induced anisotropy. The differences between free-end and fixed-end torsion are emphasized.