The diameter of silicon carbide (SiC) single crystal grown by the physical vapor transport method has increased significantly in recent years. Process modeling has played an important role in designing and developing the large diameter SIC growth systems. The numerical algorithm incorporates the calculations of radio-frequency, time-harmonic magnetic field by induction heating, radiation and conduction heat transfer in the system, as well as the growth kinetics. The generated power density in the graphite susceptor is obtained by solving the magnetic vector potential equations, and radiative heat transfer is calculated from the integrated equations for radiation. Chemical reactions and transport of gaseous species, Si2C, SiC2, SiC and Si, are also considered. A growth kinetics model is proposed for the first time, which uses the Hertz-Knudsen equation to relate the growth rate to the supersaturation of a rate-determining vapor species, the driving force for the deposition. The theoretical predictions compare reasonably with the published experimental data. The growth rate curves are obtained as a function of growth temperature and system pressure. The growth kinetics is greatly influenced by the inert gas pressure, temperature and temperature gradient. Since the vapor pressure is an ascending function of the temperature, for low temperature growth, a larger temperature gradient is needed in order to achieve the desired level of supersaturation (or growth rate). A low temperature growth is usually associated with small diameter systems, which maintain larger temperature differences. At a high growth temperature, since the vapor pressure is high, only a small temperature difference is required to achieve the same level of supersaturation. Desirable growth temperature and growth rate profiles can be obtained across the seed surface by optimizing the furnace components, such as the graphite susceptor, induction coil, and insulation materials.