A melt flow taking place during growth of Y3Al5O12 crystals by the Czochralski method including the Marangoni convection is analyzed using a finite element method. The presence of even weak Marangoni convection strongly affects the flow pattern and temperature distribution in the YAG melt. A superposition of thermocapillary and buoyancy forces causes the interface to be 20% more convex towards the melt compared to that situation without Marangoni convection. This effect is more pronounccd if the melt level is low. A quasi-planar interface is obtained by using higher rotation rates if Marangoni convection is not included in the analysis. However, the planar interface cannot be easily achieved even if small Marangoni convection is present; the interface is concave at the centre and convex at the edge of the crystal causing the whole interface to be wave-like in shape. Such shape of the interface indicates difficulties in determining a point of interface inversion.