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This paper concerns the modeling of the solidification process including the phenomena of heat transfer and fluid flow during the initial stage of the metal casting process. During this period, the molten metal motions have an essential influence on solidification kinetics. An analysis of solidification kinetics, by determining the velocity and temperature fields in a system of riser-casting was made. Velocity fields were obtained by solving the momentum equations and the continuity equation, while the thermal fields were obtained by solving the conduction equation containing the convection term. In the numerical simulations, coupling of the thermal and fluid flow phenomena by changes in the thermophysical parameters of metals alloy depending on the temperature has been taken into consideration. After completion of the filling process the main solidified of molten metal takes place and its shrinkage. The phenomenon of casting shrinkage cannot be avoided. However, it is possible to minimize the occurrence of its negative effects on the casting. One approach is to design the mould in such a way that the solidification proceeds in accordance to the assumed direction. Generally, the aim of search is to obtain a casting without shrinkage defects.