This work reports a set of approximate analytical solutions describing the transient process of gravity-induced close-contact melting between a rectangular parallelepiped solid and a flat plate on which either constant temperature or constant heat flux is imposed. Not only relative motion of the solid block tangential to the heating plate, but also the solid-liquid density difference is incorporated in the model. Normalization of the model equations in reference to the steady state admits compactly expressed analytical solutions, which agree excellently with the available numerical data. Based on the normalized liquid film thickness that is independent of the parameters, the transient time duration of close-contact melting is defined uniquely. The present solution is also capable of resolving distinctive behaviors of the solid descending velocity at the early stage of melting. A geometric function characterizing the three-dimensional effect is introduced, and its properties are clarified. It is found in the case of constant contact area that as the cross-sectional shape deviates from square, heat transfer is at least enhanced at the expense of the increase in friction between two solids. (C) 2000 Elsevier Science Ltd. All rights reserved.