Abstract: Based on the Hvorslev’s envelope-based three-dimensional elastoplastic constitutive model proposed by Yao et al. for over-consolidated clays, an acoustic tensor and a discriminator of bifurcation for strain localization under undrained conditions are given in an explicit form. The analytical and numerical solutions to the model under different stress paths are resolved. The theoretical analysis shows that onset of bifurcation occurs in the hardening regime at the Lode angle in the range of - 23.5^o ~ 4^o when the material is single-phase. There is no bifurcation occurring at the Lode angle in the ranges of - 30^o~23.5^o and 4^o~ 30^o. On the other hand, onset of bifurcation occurs in the softening regime at the Lode angle in the range of - 23^o ~ - 1^o when the material is two-phase consisting of soil skeleton and water, and there is no bifurcation occurring at the Lode angle in the ranges of - 30^o~23^o and - 1^o~ 30^o. The numerical simulations of cubic specimens of the single-phase and water-soil coupling saturated porous media under undrained condition for the bifurcation are carried out by use of a nonlinear finite element analysis software ABAQUS with the above model being implemented. A comparison indicates that the numerical results agree with the theoretical solutions.