Summary: Smoothed particle hydrodynamics (SPH) method is robust to deal with the problems of impact dynamics. Conventional SPH (CSPH) method converts the kernel integral into a volumetric weighted sum straightforwardly and it is named as particle approximation. This method is very simple and pellucid, but it causes phenomena of tensile instability and numerical oscillations and makes the numerical calculation difficulty. Modified SPH (MSPH) method employs the Taylor series instead of volumetric weighted sum and improves the way of discretization. MSPH can suppress the numerical oscillations and alleviate the tensile instability. The basic ideas of applying CSPH and MSPH methods to stress propagation problems and some application examples are presented in this paper. The numerical results are compared with those of analytical method, which indicates that MSPH can simulate the stress propagation problems accurately.