The flow that results when a shock wave in a dusty gas is reflected from a rigid wall is studied theoretically. By applying an idealized equilibrium gas analysis, it is shown that there are three types of shock reflection. The incident shock wave and the reflected shock wave are partly dispersed if the incident shock is strong the former is partly dispersed but the latter is fully dispersed if the incident shock is of intermediate strength and both of them are fully dispersed if the incident shock is weak. The equations of motion are also solved numerically with a modified random-choice method involving an operator splitting technique to study the time-dependent non-equilibrium flow. The results demonstrate the details of the formation of the reflected shock wave for the three types described.