The hypothetical accident approach to analysis of fast reactors has been applied to the meltdown of an entire core and its interaction with containment floor materials of construction. The objective has been to show that penetration can be limited by the use of low melting point fluxing materials and thermal insulation at the pool boundaries. The growth of a hemispherical molten pool composed of fuel dissolved in molten basalt is predicted by a model that includes fuel solubility, internal convection in the pool, and transient conduction into the surrounding solid. Core sizes ranging from 3000 to 20 000 kg were investigated. Tentative conclusions are: A molten pool formed by reactor fuel debris can be shown to reach a manageable limiting size rather than penetrating to an indefinite distance in an uncontrolled manner. The use of sacrificial materials in which fuel is soluble reduces pool temperatures by diluting fission product decay heat generators and increasing heat transfer surface. During the first 100 to 200 h after meltdown the storage of heat in the molten pool can reduce the fission product heat that appears in the overlying sodium pool by 50 to 75%, The use of refractory insulation can reduce the pool size and still maintain temperatures beyond the refractory boundaries at values compatible with ordinary containment structural materials.