Transient melting of a subcooled vertical wall as a result of condensation of pure vapor at its saturation temperature is investigated analytically. Using a Nusselt-type analysis, the equations governing the laminar melt and condensate films are solved by a combination of analytical and numerical techniques. Three different situations are considered: First when the condensate and the melt are of the same species and melting of the solid occurs upon first contact with the vapor; second the same as the first but when the condensate and the melt are of different species; and third when the condensate and the melt are of different species but the initial wall contact temperature is below the melting temperature of the solid. The time to achieve a steady-state condition is also evaluated.