The paper is dedicated to the mathematical modelling of Claus reaction performance in the packed catalyst bed under conditions of sulfur condensation and evaporation. The proposed mathematical model accounts for heat and mass transfer between reaction gas and solid catalyst, condensation and evaporation of sulfur, reversible catalyst deactivation by liquid sulfur, Claus reaction reversibility, intraparticle diffusion Limitations, heat conductivity of the catalyst bed frame. Reverse-flow operation of the catalyst bed have been investigated. The complex process flow-sheets, comprising two and three catalyst beds with intermediate sulfur condensers, have been simulated. It has been shown, that application of the reverse-flow technique provides increase of process efficiency.