The main emphasis of the present study is to construct an analytical solution subjected to weak shock-jump conditions (R-H conditions) for the propagation of a one-dimensional adiabatic flow of non-planar weak shock waves in a two-phase gas-particle medium (mixture of non-ideal gas and small solid spherical dusty particles). By taking into account the methodology used by Murata, the influence of mass concentration of solid particles and van der Walls parameter of non-idealness has been reported explicitly on the exact solution of flow parameters and total energy of the flow field behind the shock front. Also, an investigation has made for the estimation of radius of shock front and results has been illustrated via figures. It has been observed the radius of shock front (damage radius) attenuates faster with time on increasing the impact of mass concentration of solid particles and volumetric parameter in the mixture.