We have developed a kinetic Monte Carlo numerical scheme, specifically suited to simulate structural transitions in crystalline materials, and implemented it for the case of epitaxial graphene on SiC. In this process, surface Si atoms selectively sublimate, while the residual C atoms rearrange from a position occupied in the SiC hexagonal lattice to the graphene honeycomb structure, modifying their hybridization (from s p 3 to s p 2) and bond partners (from Si-C to CC). The model is based on the assumption that the Monte Carlo particles follow the evolution of their reference crystal until they experience a thermally activated reversible transition to another crystal structure. We demonstrate that, in a formulation based on three parallel lattices, the method is able to recover the complex evolution steps of epitaxial graphene on SiC. Moreover, the simulation results are in noteworthy agreement with the overall experimental …