Abstract: Based on the results of test under complex stress, the relationship of stress-strain under the principal stress with different directions is studied through experiments, and according to this, combined with the concept of state, an elasto-plastic constitutive model based on relationship of stress-dilatancy and simulated hyperbolic relationship of stress-strain is put forward. The effect of direction of the principal stress on the effective stress path and the evolution mode of stress-strain is described by use of simulated hyperbolic relationship of stress-strain. The experimental parameters are determined by conventional triaxial tests. It is shown by comparison between the calculated and measured results that introducing the state parameters based on the concept of state and using the effect of the direction of principal stress on the plastic modulus, the effect of the initial physical state and initial anisotropy on the stress-strain relationship of sand can be described.