Abstract The general mathematical structure of the typical multiple-source plume model for estimating concentrations of an inert air pollutant in an urban area is examined. The fundamental component is the short-term three-dimensional spatial concentration distribution resulting from a single elevated point source. From this the total pollution pattern is obtained by superposition of the effects of the individual plumes of the many point- and area-sources that constitute the urban emissions. However, superposition of the effects is generally required for time-changing emissions and also meteorological conditions. The simplifying assumptions that are basic to the short-term plume model are identified, and the frequency distribution of concentration values at a receptor location, and the long-term average values are considered. Special consideration is given to the use of the well-known Gaussian-plume and its modification when the depth of the urban mixing layer is limited. As a typical point-source plume is normally narrow, considerable simplification is possible in evaluating the concentration contribution from area-source emissions and this narrow plume approximation is described. When the emissions and the meteorological conditions affecting plume dispersion are uncorrelated, the average concentration can be calculated directly in terms of average emission rates and a frequency function for the meteorological conditions. The values so derived using the short-term multiple-source plume model are mathematically consistent with the formulation provided by an earlier long-term climatological model of urban air pollution.