A model is developed to understand the morphological stability of a SiC film on a Si substrate during carbonization where the Si substrate is exposed to a carbon precursor. The morphological stability is determined by considering the surface evolution along a slightly wavy film surface and film-substrate interface. The morphological evolution along the film surface is dominated by surface diffusion and along the interface by a chemical reaction. The kinetic analysis shows the stability is controlled by the film surface energy, the interface energy, the diffusion-reaction process of the carbon precursor, and the strain energy. At small wavelengths of the surface profiles, the two types of surface energy dominate, which results in stable morphology. The diffusion-reaction process dictates the surface stability at large wavelengths. The strain energy may cause the surfaces to become unstable at moderate wavelengths; the instability can be completely suppressed by the diffusion-reaction process and the film surface energy, while it is enhanced by a large value of interface energy.