During severe light water reactor accidents like Three Mile Island Unit 2, the fuel rods can fragment and thus convert the reactor core into a large particle bed. The postdryout meltdown of such debris beds is examined. A two-dimensional model that considers the presence of oxidic (UO2 and ZrO2) as well as metallic (e.g., zirconium) constituents is developed. Key results are that (a) a dense metallic crust is created near the bottom of the bed as molten materials flow downward and freeze; (b) liquid accumulates above the blockage and if zirconium is present, the pool grows rapidly as molten zirconium dissolves both UO2 and ZrO2 particles; (c) if the melt wets the solid, a fraction of the melt flows radially outward under the action of capillary forces and freezes near the radial boundary; (d) in a non wetting system, all of the melt flows into the bottom of the bed; and (e) when zirconium and iron are in intimate contact and the zirconium metal atomic fraction is >0.33, these metals can liquefy and flow out of the bed very early in the meltdown sequence.