This study focused on the application of Monte Carlo Simulation(MCS) in the prediction of atomic locations of alloying elements in some Ni-base single crystal superalloys. MCS based on the direct exchange of nearest neighbouring atoms was conducted by employing the Lennard-Jones pair potential, and a new algorithm optimised for vector computers was developed. For Re-containing Ni-base superalloys TMS-71 and CMSX-4, the γ and γ′ phase compositions and the site occupancy of alloying elements in the γ′ phase under equilibrium conditions were predicted by MCS, and the predictions were then compared with the estimates obtained by the Cluster Variation Method(CVM) and the experimental results obtained by atom-probe field ion microscopy(APFIM), so as to verify the applicability of MCS. It was found that the MCS estimations were generally in good agreement with both CVM predictions and APFIM results. It was also revealed that the changes in numbers of nearest neighbouring atom pairs as a function of Monte Carlo steps well describe the characteristics of alloying elements, such as partitioning and site occupancy behaviour. In addition, the drastic increase in Mo-Re nearest neighbouring pairs in TMS-71 and Cr-W pairs in CMSX-4 suggested the formation of Mo-Re and Cr-W clusters, respectively. These clusters may be a sign of precipitation of a third phase such as Topologically Close-Packed(TCP) phase. It was thus concluded that MCS is useful not only in predicting the atomic locations of alloying elements in the γ and γ′ phases, but also in discussing the possibilities of third phase precipitation and the clustering of elements, etc.