Torsion experiments were carried out on pure magnesium (99.9%) and the magnesium alloy AZ71 under free-end conditions of testing. The alloy had an axisymmetric initial texture, while the pure Mg samples were prepared from a rolled plate with a nonaxisymmetric initial texture. The torque as a function of the twist angle was measured at different temperatures (room temperature, , and ). During twisting, systematic shortening of the samples was observed (Swift effect). The evolution of the crystallographic texture was analyzed by electron backscattering diffraction measurements. The occurrence of dynamic recrystallization (DRX) was detected in pure Mg at . The Swift effect in the axisymmetric samples was simulated with the “equilibrium equation” approach using polycrystal modeling. In the nonaxisymmetric samples, the texture was simulated at different angular positions with the help of the viscoplastic self-consistent model. The changes in the textures due to DRX were explained in terms of the Taylor factor. Finally, the texture evolution was interpreted with the help of the behavior of ideal orientations and persistence characteristics of hexagonal crystals in simple shear.