A constitutive model of soil based on the generalized potential theory is rigorously developed, so that the deficiencies of traditional constitutive theories can be overcome, while the traditional theories can be regarded as its special cases. Hence the generalized potential theory provides an alternative approach to developing the constitutive model of soils. Duncan-Chang model based on the generalized Hooke’s law is one of the most widely used models at present, in which the constitutive parameters can be determined conveniently and have clear physical meanings. However, this model cannot describe well the soil dilatancy, which is the most undesirable feature of Duncan-Chang model. In addition, the hyperbolic hypothesis is adopted to fit the experimental results using Duncan-Chang model, which is also one of the disadvantages of the model. To utilize the advantages of Duncan-Chang model and avoid its disadvantages, a numerical elastoplastic model based on the generalized potential theory is developed, in which the parameters can be determined as conveniently as those of Duncan-Chang model. Meanwhile, the proposed model is not subjected to the limitation of the generalized Hooke’s law, and the soil dilatancy of soils can be well described. In addition, because the proposed model adopt a numerical method to fit the experimental results, it excludes the disadvantage of hyperbola hypothesis in Duncan-Chang model, resulting in a more adaptability of the proposed model. The performance of the proposed model is illustrated through simulating the triaxial testing results, showing that the proposed model yields good results, which describes well the soil dilatancy.