This paper presents a numerical model of multi phase flow of the mixtures of molten materialliquid-vapor, particularly in thermal nonequilibrium. It is a two-dimensional, transient, threefluid model in Eulerian coordinates. The equations are solved numerically using the finite difference method that implicitly couples the rates of phase changes, momentum, and energy exchange to determine the pressure, density, and velocity fields. To examine the model's ability to predict an experimental data, calculations have been performed for tests of pouring hot particles and molten material into a water pool. The predictions show good agreement with the experimental data. It appears, however, that the interfacial heat transfer and breakup of molten material need improved models that can be applied to such high temperature, high pressure, multi phase flow conditions.