The propagation of strong normal shock waves into a quiescent suspension composed of argon gas, water droplets and solid dust particles is studied. For evaluating the flow behaviour in the relaxation zone, the conservation equations for a steady, one-dimensional suspension flow are formulated and solved numerically. The solution indicates that the presence of water droplets and dust particles has a significant effect on the fiow inside the relaxation zone and on the eventually reached post-shock suspension equilibrium state. Higher pressures and temperatures are obtained in the suspension as compared with a similar pure pure argon case. Changes in the physical properties of the dust have noticeable effect on the dust behaviour in the relaxation zone. However, these changes have only small effect on either the behaviour of the gaseous phase or the eventually reached post-shock suspension equilibrium state.