To simulate the impact response characteristics effectively and provide reliable data for the safety prediction of explosives, the numerical simulations of the drop test and the Steven test of explosive were performed by the finite element method (FEM) and the coupling algorithm of FEM and smoothed particale hydrodynamics (FEM-SPH) and the discussion and comparative analysis for the advantages and disadvantages of all kinds of algorithms were carried out. Results show that the FEM-SPH coupling algorithm can more effectively simulate the mechanical response problem of viscous explosives after being impacted and the accuracy is higher. In the simulation of drop test, the ascending rates of pressure curve and overloading curve obtained by FEM-SPH coupling algorithm are closer to the measured values. The maximum pressure error is approximately 4%, while the error of FEM is 16%. In the simulation of Steven test, the pressure history curve obtained by FEM-SPH coupling algorithm is more consistent with the testing value. The deviation of the pressure integral value and the experimental value is approximately 10.7%, whereas the deviation of FEM is 29%, and the phenomenon after being impacted is more similar to real test situation. FEM-SPH coupling algorithm can show the relative slippage and flow characteristic of viscous materials and granular ones in the process of impact loading in a certain degree, the problems of simulating large deformation of viscous explosives after being impacted have certain advantages.