This work presents the results of a numerical study of the working processes of burning lignite in a vortex furnace with swirling countercurrent flows. The results of computer simulation of the processes of burning lignite with a moisture content of 30%, an ash content of 20% and 35% and a higher calorific value of Qрв = 13.9 MJ/kg and 9.7 MJ/kg, respectively are given. The fields of temperature distribution, gas velocity and particle trajectory in the volume and at the outlet of the furnace are determined. The values of the swirling flow velocity near the exit from the furnace reach 150-170 m/s. Mechanical underburning is 3.7% and 9.4% depending on the ash content. The results of a numerical study have showed that the diameter of lignite particles affects their combustion process: coke particles with an initial diameter from 25 microns to 250 microns burn out by 96%. The furnace provides a complete combustion of pulverized coal particles - 99.8% and of volatiles - 100% at volumetric heat stress in the 2500 kW/m3 furnace. The afterburning of fuel particles containing carbon is ensured by their circulation