A numerical model is presented to determine hydraulic and solids residence times and effluent concentrations from activated sludge reactors systems. Mass balance equations for biomass and substrate are numerically solved to determine the effects of different variables. Dimensionless quantities and computer techniques are used to express the results generally. Monod kinetics and reactors-in-series principles are applied to explain variations in axial dispersion and wastewater quality experienced in real systems. By means of the numerical approach, the variation of the ratio between the hydraulic residence time of a given reactor and that of an equivalent plug-flow tank with the same inlet and outlet conditions is investigated. Using the numerical results obtained, graphs are plotted for designing plug-flow activated sludge systems. Experimental data reported in literature is also evaluated to demonstrate the cases where the existing classical solution to the problem differs from the exact results.