Abstract. Self-similar solutions are obtained for one- dimensional isothermal and adiabatic unsteady flow behind a strong spherical shock wave propagating in a dusty gas with or without self-gravitational effects. The shock is assumed to be driven out by a moving piston and the dusty gas to be a mixture of non-ideal (or perfect) gas and small solid particles, in which solid particles are continuously distributed. It is assumed that the equilibrium flow-conditions are maintained and variable energy input is continuously supplied by the piston. The density of the ambient medium is assumed to be constant. The effects of an increase in the mass concentration of solid particles to the initial density of the gas, the parameter of non-idealness of the gas in the mixture, and the presence of self-gravitational field are investigated.