The silicon carbide SiC semiconductor material is proving today, from intense scientific and industrial development, its potential to replace and outperform silicon in several or all electronic devices for high power, high frequency and high temperature applications. However, at present, the material quality still remains an obstacle to a commercial breakthrough of a SiC technology and the improvement of the structural properties together with the increase of the available size of SiC wafers are key areas of research and development in this field. The continuing improvement of the quality of crystals obtained by the seeded sublimation growth technique, the so-called "Modified Lely Method", observed so far are mainly the results of extensive experimental work. However, different computational tools have allowed to obtain important additional information to the wide experimental knowledge. The phenomena involved in the sublimation growth process are quite complex, they include heat transfer by electromagnetic heating, radiation, conduction and convection, multicomponent gaseous species transport and gas surface chemistry. An accurate modeling of the sublimation growth process needs a code taking into account all these phenomena. Our modeling work is too recent to propose such a code as a black box. However, some parts of it like magnetic and thermal modeling coupled with simple chemical models have reached maturity. In this presentation we will mainly describe the kind of information which may be routinely obtained with this simulation tool with special emphasis on the shape control of the growing ingot.