Abstract: Although the non-coaxial models based on the traditional vertex theory can capture the non-coaxial behavior of sand, they contain some theoretical defects. An improved vertex theory is proposed and added to the state-dependent dilatancy model for sand, thus a new non-coaxial sand constitutive model is established. In this model, the non-coaxial plastic deformation is given only under loading conditions involving the change of the principal stress direction, which overcomes the shortcomings of the traditional vertex non-coaxial models. The implicit stress integration algorithm and consistent stiffness tensor of the model are given, and then the algorithm is verified by the simple shear experiment on Toyoura sand. Finally, the bearing capacity of strip foundation is analyzed by using the established model. The predicted results show that the introduction of the non-coaxial plasticity reduces the overall stiffness of the foundation model and results in a softer mechanical response, and neglecting the non-coaxial influences may lead to unsafe design.