In this paper we analyse the transient condensation process of saturated vapor in contact with one surface of a vertical thin plate, caused by a uniform cooling rate on the other surface of the plate, applied at a time t = 0. The effects of longitudinal and transversal hear conduction, as well as the thermal inertia for the plate, are considered. The nondimensional governing equations are reduced to a system of four partial differential equations with six nondimensional parameters. The transient evolution of the condensed layer thickness and the temperature of the plate are obtained using different realistic limits,including the cases of very good and poor conducting plates.