The solidification of alloys has been treated as a heat conduction problem involving moving boundaries by many workers. However, the previous treatments of this problem needed a simplified assumption about the solid phase distribution in the freezing region. The necessity of making such assumptions is due to the fact that the solution for the treezing region is complicated because of an interdependence of the heat flow and the rate of solid phase formation. That is, the heat flow is modified by the generation of the latent heat of solidification the amount of which is dependent on the rate of solid phase formation which in turn is governed by the rate of heat extraction from the freezing region. The purpose of this work is to present a solution to this problem by taking into consideration the coupled effect of heat flow and the rate of solidification. The numerical solution for the freezing region is matched, through a trial and error method, with the analytical solutions obtainable for completely solid or liquid regions. The application of a numerical method for the solution of the freezing region can be possible because the rate of solid phase formation is expressed as a function of temperature by the application of the assumption of complete mixing of solutes within a small element in the liquid phase; the use of Scheil’s equation. As the result of calculations, not only the temperature change for the entire region and the velocities of moving boundaries, but also the solid fraction within the freezing region and the shape of the dendrites based on it were obtained. The results of calculations showed good agreement with the experiments using the H₂O-NaCl system.