A mathematical model for gas flow dynamics and heat and mass transfer processes occuring in the tuyere raceways and in the zone of the final for- mation and heating of pig iron and slag has been developed and simulated on a digital computer. It takes into account the formation and size of the raceway zones, combustion of coke and its substit- utes, oxidation of the metal, radiation from the gases to the raceway boundaries, physical heat losses and the direct reduction of the pig iron elements below the raceway zones. To evaluate the distribution of heat produced by the oxidation of metal between gases and prod- ucts of smelting, the problem of heating the mat- erials in the raceways with the sources of heat in the materials under conditions of intensive gas circulation in the raceways is solved. To determine the amount of heat transferred by radiation from the gas to the boundaries of the raceways, the problem of radiant heat transfer be- tween two grey bodies forming a closed system is solved. Using the structural parameters of the furn- ace, the inlet parameters of the combination blast and exit parameters of the melt, the model permits the calculation of the temperatures of materials entering and leaving the raceways and also the res- idual temperature of the gases, which qualitatively differs from the theoretical combustion temperature. Analysis of the operation of several different blast furnaces has shown that the overall picture of the interaction between gas flow dynamics, mass and heat transfer processes occuring in the race- ways and in the zone of final product formation, obtained with the aid of the model, now permits us to approach from a different position the deter- mination of the limiting factors in furnace operat- ion. It also allows us to explain certain phenom- ena observed in blast furnace practice and to dis- cover new relationships which may be used in analy- sis and control of the smelting process.