Flooding of the reactor vessel cavity 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 vessel lower head containing molten core material is numerically investigated using a two-dimensional implicit finite difference scheme. Results are obtained for the vessel shell temperature, pool temperature, and crust thicknesses for both unsteady and steady-state conditions. For both cases, the thermal behavior of the vessel lower head is investigated by parametrically changing the emissivity of the pool surface, the vessel wall, and the upper structure and by changing the temperature of the upper structure. For a certain set of parameters, nucleate boiling on the outer surface of the vessel wall is effective in lowering the temperature of the inner wall of the vessel below the melting temperature of steel. Steady-state results are obtained by using two different heat transfer correlations for the natural convection in the molten pool, which helps in understanding how uncertainties in the modeling of physical processes can influence the evaluation of accident management strategies.