This report describes a numerical method based on the best gradient-transfer theory currently available for computing pollutant concentration distributions downwind from a stack. The vertical inhomogeneity of the atmosphere and ground roughness are included in the model. Vertical wind and temperature profiles are calculated numerically from given values of ground roughness and wind speed and relative temperature at stack height. An equation governing the plume from the stack is solved by a finite difference method. The numerical results, compared with several experiments, suggest that ground roughness is an important parameter and that is agreement between different sets of experimental data may be due to different values of this parameter. The effect of wind is found to be small under neutral conditions. The effective mean wind decreases to a minimum value a short distance from the stack and then increases downwind.