A simple and comprehensive method for describing the influences of the intermediate principal stress σ₂ and the stress histories on the deformation and the strength of soils, which assumes associated flow rule and obeys isotropic hardening rule in modified stress space, is proposed. The concept of the modified stress t_ij, which was proposed to describe the influence of σ₂, is extended to the proposed modified stress tensor t_ij^* to consider the fabric change of soils due to the stress histories as well as the variation of σ₂. In this paper, the modified stress t_ij^* is applied to an elastoplastic model named subloading t_ij model. The proposed model is verified by comparing the calculated results with the experimental results on sand.