Thin graphite films attract significant interest due to their unique physical properties and potential applications. Chemical vapor deposition in the presence of metal catalysts is one of the most promising and widely used techniques to produce these films. There are many experimental works devoted to the material synthesis; however, the results are usually obtained by the trial-and-error method without a proper understanding of the processes behind the experiment. We theoretically analyze the carbon diffusion processes inside a metal substrate during the deposition. The theory allows interconnection of the deposition parameters with the thickness of produced graphite films. Numerically solving the diffusion equations for the real systems, we obtained a good correlation between simulations and experimental data. Based on our simulations, we made some conclusions about the formation of graphite films by the precipitation process. The numerical simulations were mostly done for the popular nickel substrates, but we also made some calculations for iron, showing that it also could be used to form thin graphite films under certain conditions.