Recently, an advanced technique for growing free-spreading SiC bulk crystals by sublimation has been demonstrated. This method was used to grow 6H- and 4H-SiC boules free of polycrystalline deposits on the crystal periphery, up to 35 mm in diameter with the micropipe density less than 20 cm-2 and the dislocation density about 102-103 cm-2. In this paper, we report on the numerical modeling of free-spreading crystal growth. We consider the global heat transfer in an inductively heated growth system, species transport in the growth cell and in the powder charge, and thermoelastic stress, focusing on the crystallization front dynamics, poly-SiC deposition, and powder source evolution. Special attention was given to the validation of the simulations. The computed thermal field and evolution of the powder and crystal shape were found to agree qualitatively with observations.