A Monte Carlo surface kinetics model has been developed to predict growth rate, morphology, and the atomic content of thin films of various SiC polytypes (3C, 2H, 4H, 6H). The model represents the crystal lattice on a structured mesh which retains fixed atom positions and bond partners indicative of a perfect crystal lattice. Specified events occurring at different rates and probabilities change the configuration and the atomic content of the lattice. Events in the model include precursor transport to surface, adatom adsorption, diffusion, and desorption from surface, growth and etching reactions between adatoms and lattice atoms, and evaporation. The initial validation of the model for SiC consists of replicating trends seen when experimentally growing polytypes of SiC (111) on circular mesas and on off-axis vicinal planes. The model can predict the (111) plane faceting seen in beta-SiC and the hexagonal structures seen when growing on alpha-SiC. Also; step flow growth rates which change with flow direction are predicted by the model. Step flow growth on a (111) plane in (11 (2) over bar 0) directions is faster than growth in (1 (1) over bar 00) directions. The model is used to investigate step bunching. Step bunching is shown to be due in part to the growth rate variability of (1 (1) over bar 00) directions and the hexagonal. stacking content in the alpha-SiC polytype. The chemical variation of the step risers in the step bunch could lead to reaction rate limited growth of some steps over others leading to further bunching. The model is used to predict growth rate differences between the Si and C face of SiC. The face growth rate differences are a function of the SiH4 and CH4 surface reaction probabilities.