The constitutive model based on the generalized potential theory is established directly by mathematical methods

and the complicated concepts such as plastic potential functions in traditional plasticity theory are avoided

which gives a new approach to study the soil constitutive model. Through the multi-potential surface model in stress space of the generalized potential theory

mathematical principle of the energy equation hypothesis in the Cam-clay model is analyzed and a similar Cam-clay model is established by mathematical methods

in which the modified Cam-clay model etc. can be regarded as its special cases. Rationality of the proposed model is verified through experimental data under the condition of different stress paths; and it is also compared with the Cam-clay model. The results show that parameters of the proposed model can be determined conveniently and freely; and the calculated results agree with experimental ones

which even better than those calculated by the modified Cam-clay model. Mathematical principle of the proposed model is more clear and the difficulties and errors which are brought by the determination of plastic potential functions and energy equation are avoided; it is proved that the proposed model has better practical value.