The random choice method (RCM) has been used to calculate non-linear wave propagation in gas-vapour-droplets mixtures. The theoretical model of heterogeneous nucleation and droplet growth is discussed. The equations for wave propagation are formulated in such a way that only one source term due to condensation or evaporation remains. The specific source term properties are investigated and the implementation of the source term into the RCM by operator splitting is explained. Numerical calculations for an unsteady centred rarefaction wave and a shock wave are compared with experimental data. The formation of a condensation discontinuity is demonstrated.