Abstract: The mechanical properties of sand are influenced by void ratio and compression pressure. Based on the sand critical state line characteristics, this paper describes the isotropic compression line by means of the linear relation in e-(p/p_a)^ξ space. A reference compression curve which is more suitable for describing the isotropic compression of sand is proposed by comparing the relationship between two different compression curve functions and critical state line functions, and the isotropic hardening rule based on the reference compression line is given. A yield surface function suitable for describing the mechanical properties of sand is proposed and a method for determining the yield surface shape parameter μ using isotropic compression and equal p paths is given. To get the potential strength M_f and the characteristic state stress ratio M_c, describe the sand compression and shear characteristics, the compression curve corresponding to stress ratio is taken as the reference curve of sand. The correlation between the current stress ratio and the reference curve of state parameter is proposed based on the isotropic compression and constant p path. Consequently, a smooth transition from reference compression curve to critical state line for the reference curve of state parameter is achieved. The established 11 parameters of the sand constitutive model can all be obtained through routine geotechnical tests or experiences. The sand constitutive model established in this paper describes well the compression and shear characteristics of Toyoura sand in different void ratios and pressures based on the model prediction, isotropic compression tests, triaxial drained and undrained tests of Toyoura sand.