Polymer bonded explosive (PBX) is a typical particle-filled elastic material, and its mechanical properties are closely associated to the loading rate and strain history. The cyclic loading and unloading stress-strain curves of cast PBX in the quasi-static strain rate range of 10^-4-10^-2/s were obtained by a material testing machine. The constitutive behavior of the PBX was analyzed by Dorfmann and Ogden′s model. Results show that the PBX has loading rate effect, there are stress softening and hysteresis phenomena during cyclic loading, and residual strain phenomenon exists in the unloading process. Material damage can be characterized by hysteresis and the size of residual strain, and the damage extent is mainly affected by the maximum loading strain control. In the Dorfmann and Ogden′s model, the shear modulus μ is only affected by loading rate. The values of μ at 10^-4, 10^-3/s and 10^-2/s are 43.94, 56.92 MPa and 71.93 MPa, respectively. The model can better describe the stress softening and residual strain behavior of the PBX. The prediction results are in good agreement with the experimental data.