A mathematical model of calculating the reverberatory furnace that allows one to select the optimal ways for its reconstruction is developed. The efficiency of using the dynamic zonal-nodal method of calculation, or the method of two grids, is shown. The mathematical model is adapted to existing technological conditions, and the results of calculations are compared with the experimental data. One important feature of the developed model is the simulation of the supply and the distribution of finely dispersed cinder with an average particle size of 70 μm in the working space. The effect of the cloud of dust particles on the detail pattern of the complex gas-dynamic and thermal processes in all points of the furnace space is investigated. The calculated and experimental data fit well, which allows one to confidently use the developed model for determining the optimal design and mode parameters in its reconstruction.