Abstract: Abstract The test shows that stress-strain relationship of saturated sand has significant dependence on density and confining pressure. The above two factors can not be ignored to describe the deformation behavior of sand under static load conditions. In addition, saturated sand also exhibits obvious stress-induced anisotropy and phase transformation behaviors under complex loading, such as cyclic loading conditions. The distance $R$ between the current stress state and its corresponding point in critical state line (CSL) can be treated as a state parameter is introduced into the proposed model to reflect the density and confining pressure dependent behaviors based on the assumption that there is a unique CSL in $e$--$p$ space. The influence principle to stress-strain relationship under monotonic loading condition due to density and confining pressure is accurately described by using unified hardening parameter introduced by phase changing stress ratio and peak stress ratio expressed by exponential functions of state parameter. The shear volume compression, dilatancy, strain softening and hardening are all described for sand. By using non-associated flow rule, a water drop shape yield surface and an ellipse shape plastic potential surface are adopted in $p$--$q$ space. The liquefaction phenomenon under monotonic loading condition are also be described. To reflect the accumulation of plastic volume strain and hysteresis loops of deviatoric plastic strain under cyclic loading condition, the state parameter $R$ can be expressed as stress ratio parameter and the rotational hardening part can be adopted to describe the stress-induced anisotropy are introduced into the hardening parameter. The attenuation of shear modulus, stiffness weaken and strength decreasing behaviors are described effectively by using the proposed model. The cyclic mobility phenomenon is predicted under undrained cyclic loading conditions. The effectiveness and applicability of the proposed constitutive model is verified by the comparison of a series of simulation and test results.