The problems are considered and the results of numerical modeling of the furnace processes of heat generators are discussed. In recent decades, designs of household generators to be placed directly inside premises tend to be made more and more compact, which increases the commercial attractiveness of products, but leads to a decrease in the size of the furnace and the deterioration of conditions for the development of the flame. Based on the methods of computational hydrodynamics, a study was carried out of the furnace processes in Unimat UT-L18 “Bosch”, “FEG” Beata 2 and Vitodens 100-W “Viessmann” heat generators. The combustion of mixtures of methane with air and oxygen is considered. Geometric models of furnaces corresponding to their design features are developed. The required boundary conditions of gas fuel combustion processes in them are determined. The temperature, velocity and concentration fields in the furnaces are presented. Special attention is paid to obtaining physically adequate distributions of aerodynamic and thermal characteristics of the flame zone for each of the models made. Thermal and aerodynamic correctness of numerical calculations are a necessary condition for the adequacy of calculations of methane oxidation. Obviously, without this, it is fundamentally impossible to discuss the perfection of furnace processes in the devices studied, and in this case it has an additional significance, since the interaction of the reacting components is calculated by the one-stage oxidation scheme. Therefore, products of chemical underburning are absent, and the rate of use of fuel can only be established from the concentrations of the initial and final reagents. According to the results of calculations with confirmed correctness, a comparison was made of the completeness of the process of oxidizing the combustible components of the air-fuel mixture in furnaces, which differ in the degree of flame constraint. The created models provided the possibility of quantitative analysis of the operation of the furnace and burner devices of these heat generators. The evaluation of the perfection of furnace and burner devices, made on the basis of the results obtained, will allow the use of the most advanced types of heat generators with increased efficiency in the projects of decentralized and individual heat supply systems for buildings.