A new mathematical model of pollutant dispersion near a building has been developed. The main physical features of this Gaussian-type model include rapid mixing of pollutants inside cavities, distortion of streamlines, increased level of turbulence outside cavities, and changing dispersion regimes as a consequence of low-frequency oscillations of wind direction. The model can be used for calculation of pollution concentrations at arbitrary receptor points, including inside the cavity and on the walls and top of the building. Adjustable parameters include wind speed, wind direction and stability category as well as stack, effluent and building parameters. The model has been validated using the results of systematic studies of air pollution near buildings, which have been carried out in the EPA Meteorological Wind Tunnel. These studies have tested the effects of building aspect ratio and orientation relative to the wind flow, source height and location relative to the building, as well as effluent gas parameters (velocity and overheating). Comparison of calculated and measured vertical profiles of concentration at a distance of 15 building heights from the source have shown that the mathematical model reproduces reasonably well the simulation results (80 to 90% of calculations differ from measurements by less than a factor of two), and works better in the presence of the building than in its absence.