This research characterized the strain hardening behavior of AZ31 under different stress states from shear to balanced biaxial tension with a newly proposed yield function. Experiments are conducted for AZ31 magnesium alloy by in-plane shear specimens, dogbone specimens, notched specimens and bulging specimens to characterize the flow behavior under different stress states. The flow behaviors are characterized by a newly proposed yield function in a form of the three stress invariants. The proposed yield function is implemented into ABAQUS/Explicit to predict the plastic response of the alloy under different stress states. It is shown that the proposed yield function can precisely predict the distinct flow behaviors and reaction forces from shear to equibiaxial tension from the initial yielding to fracture.