The coupled atmosphere/crown fire behaviour model is based on conservation of mass, momentum, species and energy. The system of differential equations for crown canopy was integrated with respect to the vertical coordinate because horizontal sizes of forest are much greater than the heights of trees. As a result, it is used two systems of equations for boundary layer of atmosphere and crown canopy. These equations are solved numerically for turbulent flow with the use of diffusion equations for chemical components and equations of energy conservation for gaseous and condensed phases. The method of finite volume is used to obtain discrete analogies. The boundary-value problem is solved numerically using the method of splitting according to physical processes. It allows investigating dynamics of forest fire initiation and spreading under influence of various external conditions. In this context, a study - mathematical modelling - of the conditions of forest fire spreading that would make it possible to obtain a detailed picture of the change in the temperature and component concentration fields with time and allows determining the total CO and CO2 emissions into the atmosphere during the spread of forest fire.