Flooding of the drywell of a boiling water reactor (BWR) is one of many accident management strategies being proposed to manage severe accidents in light water reactors. The effect of external cooling on the thermal behavior of the BWR vessel lower head containing molten core material has been numerically investigated using a two-dimensional implicit finite difference scheme. Results have been obtained for the vessel shell temperature, the molten pool temperature, and the crust thickness for steady-state conditions. For each equilibrium state, the thermal behavior of the vessel lower head has been investigated by parametrically changing the emissivity of the pool free surface, the vessel wall, the baffle plate, the core shroud, and the upper structure; and the temperature of the upper structure. For a certain set of parameters, nucleate boiling on the outer surface of the vessel wall is found to be effective in lowering the temperature of the inner wall of the vessel below the melting temperature of the steel. For most cases, failure of the BWR baffle plate would occur.