Shear strain, coupled with other deformations, is inevitably involved in the forming process with severe plastic deformation. The torsional and torsion-tension coupling behaviors of magnesium alloys are investigated both experimentally and numerically. Rod specimens with different initial textures, prepared from a magnesium alloy AZ31 plate, are tested under the free-end torsion and coupled torsion-tension. Parallelly, the elastic viscoplastic self-consistent model with the twinning and detwinning scheme, in conjunction with a torsion-specific finite element approach, is employed to model the free-end torsion, fixed-end torsion, and coupled torsion-tension. The anisotropic torsional and torsion-tension coupling behaviors are captured by the model. The Swift effect, which is picky on the constitutive model, is also reproduced by the model. Furthermore, the torsional and torsion-tension coupling behaviors of magnesium alloys are understood in terms of the deformation textures, relative activities of deformation mechanisms, and the distributions of the stress, strain, twin volume fraction.