The plastic spin has recently been identified as a key concept in the macroscopic description of large deformation plasticity for the treatment of anisotropic hardening. A class of combined isotropic-kinematic hardening models is formulated here, which includes two alternative constitutive equations for the plastic spin. The various sets of constitutive equations are used to analyze the large strain torsion of solid circular bars with either axially fixed ends or free ends. These analyses are carried out numerically using special purpose finite elements and, when feasible for particular cases, by means of a semianalytical method. It is shown that the plastic spin, and its different constitutive descriptions, have a significant influence on the predicted torque response and, in particular, on the axial Swift effects. The differences between fixed-end and free-end predictions are emphasized. It is found that the difference in predicted axial effects for the various plastic spin constitutive laws is most pronounced in fixed-end torsion, while the torque response is most sensitive in free-end torsion.