The difference and similarity between Monte Carlo simulations and molecular dynamics simulations are discussed, and the combined method between the two methods is also examined. These methods are used for the study of elemental processes of thin film formation. First, the computer simulations of film growth are carried out using general expressions of interatomic potentials, i.e, the Morse function and the Lennard-Jones function. The growth mode of thin films and the structure of the interface between film and substrate are studied as functions of the energy parameters and the lattice mismatch between film and substrate materials. Next, realistic simulations of film growth are made using the embedded atom method potential, and the structure of the interface is studied for some particular materials. It has been shown that the general expressions of the interatomic potential are useful for general discussions of the growth mode of thin films, while the realistic potential is suitable for obtaining information of film growth of particular materials. Assumptions and simplifications introduced in the simulations are discussed in detail. The role of the model in the computer simulations is particularly emphasised.