This paper follows the propagation of pollution in a river with a rectangular cross-section of the river bed and a variable cross-sectional velocity. The calculations were made for steady flows and steady pollutant concentrations. To approximate the velocity distribution in the river bed a set of equations for current and vorticity functions was solved. The distribution of pollutant concentrations in the river was calculated from a bidirectional advection and turbulent diffusion equation. Analysis of the distribution of concentrations leads to the conclusion that the effects of transverse advection associated with a lateral inflow of pollutants disappear relatively quickly. Therefore, the distribution of concentrations in cross sections further downstream from the point of pollutant discharge can be determined quite accurately just from an advection-diffusion model, with no transverse advection effects included. Such a level of accuracy is usually sufficient to assess the impact of a pollution source on the aquatic environment. The transverse mixing of pollutants in the stream proceeds slowly and creates a large mixing zone in which the concentrations of pollutants (low but still significant for water quality) can be detected in cross-sections that are remote from the pollutant discharge point. Transverse advection may be ignored while calculating concentrations in remote cross sections at straight watercourse sections and in steady state conditions.