The main obstacle for the implementation of numerical simulation for the prediction of the epitaxial growth is the variety of physical processes with considerable differences in time and spatial scales taking place during epitaxy: deposition of atoms, surface and bulk diffusion, nucleation of two-dimensional and three-dimensional clusters, etc. Thus, it is not possible to describe all of them in the framework of a single physical model. In this work there was developed a multi-scale simulation method for molecular beam epitaxy (MBE) of silicon carbide nanostructures on silicon. Three numerical methods were used in a complex: Molecular Dynamics (MD), kinetic Monte Carlo (KMC), and the Rate Equations (RE). MD was used for the estimation of kinetic parameters of atoms at the surface, which are input parameters for other simulation methods. The KMC allowed the atomic-scale simulation of the cluster formation, which is the initial stage of the SiC growth, while the RE method gave the ability to study the growth process on a longer time scale. As a result, a full-scale description of the surface evolution during SiC formation on Si substrates was developed.