The numerical modeling of interaction between oxygen high-pressure jets and a liquid-metal surface in a steel-making converter, where, under the force action of the jets, a cavern with a hydrodynamically unstable surface forms in the metal bulk, is studied. A simplified scheme of chemical reactions and mechanisms of metal-drop dispersing from the interface between the phases is proposed. This scheme permits an adequate description of the hydrodynamic flow pattern in the cavern. The modeling of a two-phase turbulent flow in the cavern is considered within the framework of the continuum model based on the averaged Navier-Stokes equations. To close the equations, a modified k-epsilon turbulence model is used, which takes into account the presence of the second phase. The flow structure in the cavern is studied. Practical recommendations for increasing the efficiency of the carbon-monoxide afterburning process in the cavern are given. (C) 2011 Elsevier Ltd. All rights reserved.