The relevance. In modern scientific researchthe computing experiment is one of the most productive means of studying complex tasks where the outcome depends on simultaneous influence of aerodynamics, heat transfer and combustion. Numerical calculations allow not only explaining correctly the physical phenomena notedat experimental installations, but quite often considerably extending expensive and labor-consuming physical or full-scale experiment with computer simulation. In this regard, the relevance of research aimed at improving the methods of numerical analysis of furnace processes in boilers with circulating fluidized bedon the basis of computer mathematical modeling is very high to justify the basic design and technological decisions taken when creating boilers with circulating fluidized bed. In addition to practical significance, the research has a high scientific component, since the fundamental laws of physical and chemical processes in the circulating fluidized bed are the basis of the task. The aim of the research is todetermine the approaches and applicability of numerical algorithms with satisfactory level of detail and convergence for modeling furnace processes in boilers with circulating fluidized bed. Object: furnace with circulating fluidized bed, equipped with two inputs of fuel and inert particles on the rear wall and ten secondary airinlets on the front wall in two decks. Methods: mathematical modeling of physical and chemical processes in a furnace chamber with circulating fluidized bed based on Euler-Euler and Euler–Lagrangian approaches using RANS models.Differential equations for conservation of mass, momentum, energy and particle transport are written. The numerical study was carried out using the Ansys Fluent V. 12. 1 software package. Result. The initial and boundary conditions for numerical simulation of processes in the furnace chamber of a boiler unit with circulating fluidized bed using Euler-Euler and Euler–Lagrangian approaches are determined.