Given the formulation of material free energy, the bi-potential theory allows one to divide standard materials into 2 main categories: explicit or implicit. The Drucker-Prager (D-P) model was taken as an example, which typically describes non-associated materials through the constitutive cones. With a new description of the orthogonal law, the dual constitutive cones were proposed, which not only satisfy the constitutive law of the D-P model, but also meet the requirements of the implicit flow rules. On the basis of the D-P model, and according to the bipotential theory, 5 forms of bi-potential functions were established: the elastic stage in rate form, the plastic stage in rate form, the elastic stage in incremental form, the plastic stage in incremental form and the elasto-plastic stage in incremental form. The bi-potential integration algorithm was then obtained. A numerical simulation example was given to verify the accuracy and stability of the bi-potential integration algorithm.