Abstract: A model of two-phase equilibrium for shear bands in sand is suggested in this paper,which may be viewed as a novel bifurcation solution.The shear bands are considered as a high-strain phase and the other regions outside shear bands as a low-strain phase.Across interfaces between two phases,discontinuity of deformation gradient and stress is considered,and continuity of traction and displacements and the Maxwell relation are imposed.Governing equations for sand under plane strain loading are deduced,and the analysis is reduced to finding the minimum value of the loading at which the governing equations have a unique,real,physically acceptable solution.The Maxwell stress,the stresses and strains inside and outside the shear band,and the shear band orientation angle are determined,which are in good agreement with the experimental observations.