A fundamental problem concerning the theory of strain localization is the condition of the occurrence of localization bifurcation. Based on the Hvorslev envelopebased three-dimensional elastoplastic constitutive model for overconsolidated clay, an analytical solution of bifurcation and the expression of inclination angle for shear band caused by localization bifurcation are derived for strain localization in plane strain stress states. Meanwhile, influences of overconsolidation ratio (OCR) on the analytical solution and the inclination angle are analyzed. The theoretical analysis shows that onset of localization bifurcation occurs in the hardening regime under the plane strain conditions and, with strain localization expanding, the change in inclination angle of shear band is striking before bifurcation and steady thereafter. On the other hand, numerical simulation of plane strain tests on the isotropically homogenous cubic specimen for the bifurcation is carried out by using a finite element analysis software ABAQUS with the model implemented. Numerical solutions exhibit a good overall agreement with analytical solutions for the bifurcation onset, indicating that the analytical solutions are reasonable.