The large strain torsion of polycrystalline materials with the hexagonal close packed (HCP) crystallographic structure is numerically studied by using a special purpose finite element. All simulations are based on the recently developed large strain elastic visco-plastic self-consistent (EVPSC) model for polycrystalline materials. For the first time, the effect of twinning on the large strain torsion is assessed in the present study. It is found that the response of the large strain torsion of HCP polycrystals is very sensitive to the initial texture and texture evolution. Numerical results indicate that excluding texture evolution dramatically reduces the development of the second-order axial strain under free-end torsion, or the axial force under fixed-end torsion. It is also numerically demonstrated that twinning has a significant influence on the large strain torsion of HCP polycrystals. For the magnesium alloy AZ31 extruded bar, the predicted results are in good qualitative agreement with experimental observations.