Reverse tension-compression and compression-tension experiments are performed on an extruded AZ31B magnesium sheets using a newly-developed antibuckling device. In addition, combined tension and shear experiments are performed to investigate the material response to multiaxial loading. A constitutive model is proposed which makes use of a single crystal approach to describe the dominant twinning and detwinning response, while a quadratic anisotropic yield function is employed to model the slip-dominated material response. The model accounts for the characteristic tension-compression asymmetry in the hardening mechanisms. Both the convex-up shaped stress-strain response under twinning and concave-down shaped response for slip-dominated behavior are predicted accurately. Furthermore, the effect of latent hardening among slip and twinning systems is taken into account. Due to strong simplifications regarding the kinematics of twinning, the model is computationally efficient and suitable for large scale structural computations.