The solidification problem of a binary eutectic alloy has been treated taking both heat and solute transport into account. A numerical solution for the freezing region is matched at two moving boundaries, through a simplex method for function minimization, with analytical solutions obtainable for a pure solid or a pure liquid region. As the results of calculation, it is possible to obtain the amount of solute diffusing toward the pure liquid region, the temperature profiles within the three regions, the velocities of two moving boundaries and the distribution of solid fraction within the freezing region. The results of calculation are compared with the experimental results of solidification using the H₂O-NH₄Cl eutectic system.