A model is developed for controlling the heating and the rate of drawing of leicosapphir crystals, when grown from a liquid melt. The model operates in real-time, on modern controllers, providing a flat front of crystal crystallization throughout the process. A block diagram of the weight control system for growing leucosapphire crystals is presented based on weighing the descending melt in a crucible and obtaining a control signal in function of deviating the current crystal area from a given one. The above model control heating and crystal pulling rate of sapphire crucible stationary liquid melt operates based on reference shape of the growing crystal and the axial gradient throughout the process and allows to set the drawing speed and the power for the heating installation, before starting the growth process. On the basis of the liquid melt, which changes during the growth of the weight, a correction signal is introduced in the control system as a deviation of the varying weight of the crucible with the melt from the programmed one on the cylindrical part of the grown crystal. The control signal, as an integral component, is introduced into the heating power circuit, and as proportional to the pulling speed loop, periodically each cycle of the crystal moving by 1 mm, provides the given shape of the grown cylindrical part of the crystal. The results of this work can be used in the design and modernization of existing growth plants for the growth of leucosapphire crystals from a fixed crucible with a melt.