This paper describes a computer simulation experiment which reproduces, upon an idealized (100) cubic crystalline surface, the atomic processes occurring in condensation, evaporation, and surface diffusion. Nucleation of two‐dimensional clusters was observed. The equilibrium distribution of cluster sizes and the critical cluster size were measured for various parameter values and compared to predictions of the Walton‐Rhodin atomistic nucleation theory. Very good agreement between the simulation and theoretical values was obtained. The nucleation rate was also measured for one particular set of parameter values and found to agree satisfactorily with the atomistic theory prediction. Consequently, we conclude that the Monte Carlo method is suitable for the simulation of the phenomena of heterogeneous nucleation. Suggestions are offered for the refinement and extension of the simulation model for future simulation experiments to help answer the unresolved questions of heterogeneous nucleation theory.