As a key technology of pulse solid rocket motor (SRM), the soft pulse separation device (PSD) has become a key breakthrough in the engineering application of pulse SRM. Its deformation process is very complex, accompanied by large displacement and large strain. This paper establishes a constitutive model of rubber-like soft PSD based on peridynamics to study the large deformation. Based on this method, the deformation process of axial and radial type of soft PSD under impact load is studied. Firstly, the established peridynamics constitutive model is verified by uniaxial tensile calculation of the soft PSD material, And then the deformation process of axial and radial type of soft PSD under impact loads is predicted. The peridynamic predictions are compared with finite element analysis results. The results show that this method can effectively simulate the deformation process of soft PSD under impact load; Different forms of soft PSD have different deformation phenomenon, and the radial soft PSD exhibits buckling and instability deformation.