A significant disadvantage of grate stokers is great carbon loss. To reduce these losses, the ash caught in the flue is returned to the furnace for afterburning. The effectiveness of this measure depends on the thermal characteristics of coal, the size of the pieces of coal and ash, the degree of carbon elimination, and the design features of the combustion chamber. Normative techniques to calculate and design grate stokers do not consider the features of coal combustion with ash return. Thus, it is relevant to develop the models that describe the creation of ash flows in the boiler path depending on its design, properties and dispersed composition of the burned coal and the aerodynamics of the combustion chamber. Mathematic simulation of the processes of particle size classification has been carried out to describe the creation of ash mass flows on the grate and in the convection chamber. To evaluate the parameters of mathematical models, simulation modeling of gas dynamics of flue gases in the combustion chamber has been carried out with SolidWorks software. The authors have developed a mathematical model and the method to identify its parameters. It allows us to obtain quantitative estimates of the economic efficiency of boilers with grate firing of coal. Thus, a computer program has been developed. The authors have used the program and the Neryungri brown coal to burn in the KV-TS-30-150 boiler. The results have shown that carbon loss without fly ash reinjection is 11,27 %. Introduction of fly-coke return unit reduces the loss up to 10,45 %. It is established that elimination of slit windows in the rotary baffle will lead to a change of the trajectories of ash particles and carbon losses reduction up to 10,17 %. Limiting the maximum size of coal pieces to 50 mm will lead to a more noticeable increase of boiler efficiency. The calculations have showed that in case the value of the carbon burn out factor equals 0,935, the carbon loss when the system of fly ash reinjection is turned off, its commissioning and, in addition, an increase of the gas density of the rotary screen will be 4 ,88%, 4,44% and 4,3% respectively. In case of a more careful assessment of the burnout factor at the level of 0,9, the carbon loss will be 7,51%, 6,87% and 6,65% respectively. The developed mathematical model makes it possible to evaluate the effect of the operation of the fly ash reinjection unit on the efficiency of the operation of a boiler with a grate stoker. Validation of a model for adequacy and for accuracy increase can be carried out after field testing of the boiler equipment.