Abstract: Predictions for the onset of deformation bifurcation are critically dependent upon the constitutive equations employed. The ordinary theory of plasticity stems from the considered flow rule, which is based on the assumption of coaxiality between the directions of principal plastic deformation rate and principal stress. Due to the major deficiency, the coaxial theoretical predictions cannot explain that the decrease of shear band inclination angle with increasing confining pressure and also underestimate shear strain of bifurcation. The inadequacy has led to the development of a consistent non-coaxial plasticity theory. The present analysis supports the hypothesis of non-coaxiality. Using this theory, the theoretical predictions for shear band orientation and its shear strain at the onset of bifurcation are shown to agree well with experimental observations.