A heat and mass transfer model is proposed for the physical vapor transport growth of SiC crystals with the kinetics represented by the Hertz-Knudsen equation. The growth rate is assumed to be proportional to the supersaturation of the rate-limiting agent. A numerical algorithm has been developed that consists of 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 rate. The generated heat power density in the graphite susceptor is obtained by solving the magnetic vector potential equations. Radiative heat transfer is obtained by solving the integrated equations for radiation. The theoretical growth rate compares well with the published experimental data.