Abstract: A non-coaxial constitutive model is proposed from the elasto-plastic constitutive model based on the state-dependent critical state model considering the fabric anisotropy of sand. The bounding surface plasticity is introduced to deal with the reversal loading condition, such as pure rotation shear tests. And a potential surface is derived from the multiaxial formulation of the dilatancy equation, indicating the non-associated coaxial flow direction in the plane. In addition, the non-coaxial flow direction is redefined as the orthogonal direction of the current principal stress and is affected by plastic loading index just as the coaxial flow direction. Two types of loading modes of hollow cylindrical shear tests oan Toyoura sand are simulated by the model, namely tests with fixed principal stress axes and those with rotation of the principal stress axes. In comparison with the experimental data, the simulated results can reflect the characteristics of anisotropic plasticity and the variation of the non-coaxial phenomenon reasonably.