A non-coaxial constitutive model is proposed based on the Gram-Schmidt orthogonalization process employed in the yield vertex non-coaxial theory. The flow rule is revised in this model. The model corrects the original flow rule

where the non-coaxial flow direction is defined as the projection of the unit stress increment direction in the orthogonal direction of the reference principal stress

and is associated with the plastic scalar factor. In addition

a new form of plastic function is derived according to the dilatancy equation in the generalized stress state. Based on the state-related sand model

the new non-coaxial model and the uncorrected model are used to simulate the hollow cylindrical single shear test and the hollow cylindrical torsional shear test on Toyoura sand. The simulation results are compared with the experimental data

and the results show that new non-coaxial model can more reasonably reflect the non-coaxial phenomenon and its variation in the test

especially for the monotonic shear test in the direction of the fixed principal stress axis.