It is very important to know the dependence of the shape of crystallization front on variations in technological parameters and heat exchange near this front along the boundary “shaper – melt” for optimize the process of sapphire profiles growing. The paper gives the mathematical model of the growing of sapphire profiles that considers the variations of thermal and hydrodynamic parameters with different rates of growing within the zone of crystallization. The model uses an adaptive mesh of finite elements for sampling inside the area of phase transfer. The used variation parameters are the rate of growing, the heat extraction of the crystal and inside the thermal zone. It is possible to obtain the distribution of temperature inside the zone of growth and also the shape of crystallization front for various configurations of the thermal zone and technological parameters of growing using the model.  Parameters used for the sapphire profiles growing such as the configuration of thermal zone (the quantity and position of thermal screens), the design of shaper  and the pulling rate can be defined using the calculation data  by the model with sufficient accuracy. A period of time which is needed for testing the configuration of thermal zone while changing cross-section types of the sapphire.

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