The article deals with the numerical modeling of the processes of transfer and diffusion of air pollutants in the boundary layer of the atmosphere. A mathematical model of the spread of industrial emissions in the atmosphere was developed, taking into account the motion velocity of finely dispersed substances and a number of other factors affecting the change in the concentration of harmful substances in the atmosphere. The model is described by multidimensional partial differential equations with corresponding initial and boundary conditions. For the numerical integration of the problem, the method of splitting into physical processes (of transfer, diffusion and absorption) and an implicit finite-difference scheme of the second order of approximation in spatial variables and in time were used. A software tool was developed to conduct a computational experiment on a computer and to perform a comprehensive study of the processes of transfer and diffusion of harmful substances in the atmosphere