In this paper we study the laminar condensation process of a saturated vapor in contact with one side of a Vertical thin plate, caused by a natural laminar boundary layer flow on the other surface of the plate. The effects of both longitudinal and transversal heat conduction in the plate are considered. The momentum and energy balance equations are reduced to a system of differential equations with five parameters. Asymptotic and numerical solutions for the temperature and condensed film thickness distributions are presented for all possible Values of the nondimensional plate thermal conductance alpha.