The thermal stress distribution in growing SiC bulk single crystals is analyzed by a Finite Volume solution approach using anisotropic elasticity theory. The stress calculations are based on a global simulation of heat and mass transfer during the SiC bulk growth process. The temporal evolution of the thermal stress distribution inside the growing crystal is studied. It is found that the conditions for thermal stress formation at fixed positions in the crystal vary significantly during growth. The impact of the stress boundary conditions (free/fixed surfaces) on this behaviour is investigated. The calculated stresses exceed considerably the critical resolved shear stress in SiC which indicates that the observed dislocation formation under the established growth conditions should be caused at least partly by thermal stresses.