Abstract: The Compressive hardening, shear dilatancy and friction are the three basic mechanical properties that affect the stress-strain relationship of soils. For different types of soils, there are similarities and differences in the three basic properties. The similarities provide the possibility to establish a unified description for the stress and strain characteristics of various soils, while the differences need to be reflected by adjusting the parameters or constructing the variables in the constitutive model. The unified hardening model (CSUH model) for clays and sands is a typical representative of the unified model. It quantitatively describes the difference in the compressive hardening of different soils by adjusting the compaction hardness parameter p_s. The difference in the shear dilatancy of soils with different densities can be reflected by applying the state parameter ξ in the hardening parameter H. The difference in the strength of soils under different stress Lode angles θ is described by the transformation stress method. By comparing the measured data of several groups of clay, sand and rockfill with the predicted data of CSUH model, the results show that the CSUH model can describe the stress-strain relationship of different kinds of soils with different densities.