A mathematical model of sulfur transfer in a moving metal and slag melts has been developed. Sulfur is transported simultaneously both by diffusion and by laminar natural convection of the melting metal and oxide fluxes. The diffusion of sulfur is described by the 2nd Fick's law. We have computed the distribution of sulfur in the metal and slag phases and the concentration changes of sulfur in the volume of the metal and slag phases, both functions of space and time. Numerical results are provided to show the validity of this approach.