Large-strain elastic-viscoplastic torsion of circular tubes and solid bars of glassy polymers is investigated under fixed-end as well as free-end conditions. The analysis employs a large inelastic deformation model for glassy polymers that incorporates a recently proposed constitutive law for the so-called orientational hardening, which is identified to play a key role in the description of the deformation-induced anisotropy in glassy polymers. The solution of the problem is obtained numerically by means of simple, special purpose finite elements. 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, both phenomena being associated with anisotropic hardening. In some cases, the predicted stress distributions are also given. The differences between free-end and fixed-end torsion are emphasized. Numerical results predicted by the model are compared with experimental results for polycarbonate found in the literature.