On the basis of the mechanical properties of polymer bonded explosive (PBX), the linear Drucker-Prager model was introduced into the elastic-plastic deformation study of the PBX material. Based on the linear Drucker-Prager model, combined with the classical plasticity theory, the quasi static elastic-plastic deformation process of the PBX was analyzed. The subsequent yield surface characteristics were cleared. Its stiffness algorithm was derived. The elastoplastic constitutive model was constructed. The relationship of stress and strain under the conditions of uniaxial compression state and biaxial compression state was analyzed in theory. The unit characteristics of PBX material were simulated by the linear Drucker-Prager model. Results show that the uniaxial compression simulation results are consistent with theoretical analysis ones and experimental data. The biaxial compression simulation results are consistent with the theoretical analysis ones. By contrast, the ultimate strength of the biaxial compression is 1.16 times greater than that of the uniaxial compression. Corresponding plastic strain is 0.5 times greater than that of the uniaxial compression.