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The monotonic and cyclic mechanical behavior of O-temper AZ31B Mg sheet was measured in large-strain tension/compression and simple shear. Metallography, acoustic emission (AE), and texture measurements revealed twinning during in-plane compression and untwining upon subsequent tension, producing asymmetric yield and hardening evolution. A working model consistent with the micro- and macro-experimental data was constructed. Plastic straining occurs preferentially by basal slip, which provides two independent slip systems with low critical resolved shear stress. The macroscopic flow stress is determined by the required activation of higher-stress mechanisms to accommodate arbitrary deformation: predominantly non-basal slip for initial tension, twinning for initial compression, and untwinning for tension following compression. The nucleation stress for twinning is larger than that for untwinning. Increased accumulated hardening increases the twin nucleation stress, but has little effect on untwinning. Multiple-cycle deformation tends to saturate after a few cycles of ± 0.02 strain, but does not saturate for ± 0.04 strain cycles by the time fracture intervenes at 10 cycles.