Purpose. Study on the possibility of extracting coal underfire particles from the ash of the thermal power station by flotation. Intensification of the enrichment process of coal particles, development of a mathematical model for forecasting indicators of the ash function. Methodology. The method of fractional flotation was used to study the kinetics of the process of extraction of the valuable component. The technique of the planned experiment was applied, including the central composite rotatable plan of the second order for four factors affecting the ash content of the coal concentrate. Findings. According to fractional analysis, the concentration limit of coal particles was determined. During the flotation of fly ash, the best results were obtained on the EFM ejector type flotation machine, the yield of the foam product was 18.6 % with an ash content of 25.1 %, compared to the MFU mechanical type flotation machine, where the ash content of the foam product was 36.5 % with an average yield of 21.1 %. The optimal consumption of reagents at the level of no more than 3,500 g/t of the collector and foaming agent up to 250 g/t was determined experimentally, and the required flotation time was determined. Calculations were performed to determine regression coefficients and the degree of influence of factors on the flotation process. A mathematical model of the flotation process of TPP ash removal was determined, which characterizes the influence of the main factors. The graphs of the significance of the factors and the three-dimensional surface of the calculated response function were drawn up. Originality. The degree of influence of factors such as pulp pressure in the feed pipeline, collector consumption, foaming agent consumption, and flotation time on the process of beneficiation of TPP ash on the EFM ejector type flotation machine was determined. Practical value. The complex model makes it possible to predict the final indicators of the response function, namely the ash content of the secondary coal concentrate. The results will make it possible to improve the parameters of technological processes for the enrichment of TPP ashes.