In order to study the quasi-static compression behavior of polymer bonded explosive （PBX）， the uniaxial quasi-static compression tests were carried out on two typical PBX substitute materials （with and without aluminum powder） at different strain rates， and their mechanical properties were compared and analyzed. Based on the Zu-Wang-Tang （ZWT） model， a new model was proposed to describe the quasi-static compression behavior of materials. The constitutive model parameters were obtained by genetic algorithm， and the model was developed by using Fortran language in the User Material （UMAT） subroutine interface of Abaqus finite element analysis software. Results show that the quasi-static compression process of casting PBX substitute materials can be divided into three stages： elastic compression， stress decay and instability failure. The mechanical behavior of quasi-static compression is obviously correlated with the strain rate. With the increase of the strain rate， the effective compressive strain of the material is basically unchanged， while the logarithms of compression modulus， yield strength and compressive strength are linearly related to the logarithm of strain rate. The addition of aluminum powder can improve the compression modulus， yield strength and compression strength of casting PBX substitute materials. The newly constructed constitutive model can better describe the quasi-static compression behavior of casted PBX substitute materials， and its universality is validated by the finite element analysis software. The coefficients of determination （R²） between the simulated and experimental results are higher than 0.98， indicating a high level of consistency.