The constitutive response of a commercial magnesium alloy rolled sheet (AZ31B-O) is studied based on room temperature tensile and compressive tests at strain rates ranging from 10 −3 to 10 3 s −1 . Because of its strong basal texture, this alloy exhibits a significant tension–compression asymmetry (strength differential) that is manifest further in terms of rather different strain rate sensitivity under tensile versus compressive loading. Under tensile loading, this alloy exhibits conventional positive strain rate sensitivity. Under compressive loading, the flow stress is initially rate insensitive until twinning is exhausted after which slip processes are activated, and conventional rate sensitivity is recovered. The material exhibits rather mild in-plane anisotropy in terms of strength, but strong transverse anisotropy (
r-value), and a high degree of variation in the measured r-values along the different sheet orientations which is indicative of a higher degree of anisotropy than that observed based solely upon the variation in stresses. This rather complex behaviour is attributed to the strong basal texture, and the different deformation mechanisms being activated as the orientation and sign of applied loading are varied. A new constitutive equation is proposed to model the measured compressive behaviour that captures the rate sensitivity of the sigmoidal stress–strain response. The measured tensile stress–strain response is fit to the Zerilli–Armstrong hcp material model.