A quasi-stationary process of directional crystallization of a binary melt with a two-phase region has been studied theoretically. The model takes into account the dependence of the melt density on temperature and impurity concentration. Exact analytical solutions of a nonlinear system of heat and mass transfer equations are obtained. The impurity concentration and temperature profiles, the crystallization rate, and the fraction of the solid phase in the two-phase region are determined. It is shown that with an increase of the initial impurity concentration in the melt, the width of the two-phase region increases.