Abstract: It has been proved that analysis of the two-dimensional pollutant concentration distribution characteristics during the expansion of contaminated zone in river-offshore discharge, and prediction of the concentration on the environmental sensitive sites have aroused a considerable attention of the academic and engineering communities. Its boundary reflection being taken into consideration based on the analytical solution of the simplified two-dimensional advection-diffusion equation for rivers, the formula of x_1.2'threshold, which categorizes the wide-and medium-wide rivers based on the relative offshore distance a' (defined as the ratio between the distance from the discharge outfall a and river width B), has been proposed through series computational experiments on off-shore discharge, concentration distribution contouring, and mathematical induction and analysis. The definition of maximum concentration axis in river cross-sections has been proposed, along with its piecewise equations applying to each sub-situation classified by certain criterion. The thresholds x_e' and x_k' separating the x-axis segment, curved segment and near-shore segment of the defined maximum concentration axis are given with a simplified calculation formula for cross-section maximum relative concentration, relative concentration along the centerline and banks of the rivers for each segment. The results afford a theoretical basis for the prediction and assessment of the river water environmental impact.