The aim of this paper is to improve our understanding of the SiC growth mechanisms from the vapor phase (bulk material or thin film). Detailed studies of bulk and surface structures are therefore needed. The geometries of hexagonal (2H, 4H, 6H) and cubic (3C) polytypes have been optimized thanks to calculations based on density-functional theory (DFT). It appears that 6H and 4H are the most stable phases, which is in agreement with other calculations, but not with experiments that indicate a preference for the growth of the cubic form on flat terraces. Thus, to analyse further the growth processes, we began an investigation of the surface of 4H SiC, which is the most interesting polytype regarding the electronic properties. Since the substrate used during the experiments is an off-oriented hexagonal SiC single crystal, we studied the morphology of the steps along the [1 (1) over bar 00] direction for C- and Si-terminated surfaces. In these particular cases, the total energy calculations show that the most stable steps are one bilayer high.