An analysis is carried out for the solidification in a rectangular enclosure whose top and bottom surfaces are kept adiabaticand sides are kept at a constant temperature. The transient effects of solidification accompanied by natural convection have been studied in detail. The governing equations are written for the temperature, vorticity, stream function and velocity in the melt along with the heat conduction equations through the solid and the mold. The non-linear coupled equations have been non-dimensionalized and solved with the aid of the Alternating Direction Implicit finite difference method. The velocity profiles in the melt, and the temperature distribution in the melt, the solid and the mold are shown. Isotherms and streamlines in the melt are plotted for different Rayleigh numbers. The dependence of the melt-solid interface movement upon various non-dimensional parameters, such as Rayleigh number (5 × 102-5/s 105 Prandtl number (0.1-100), aspect ratio (1.1-5.5), Stefan number (0.5-10) and a parameter indicating the effect of superheat (0.67-2.33) are also studied. © 1982.