A mathematical model suitable for simulating the distribution of the conservative and the non-conservative water quality of the river system in the lower Kansas River basin is described. The model consists of three digital computer programs and considers both quasi-steady-state and dynamic hydrologic boundary conditions. The hydrologic and conservative portion of the model has been tested for verification with discharge records for six time periods of from four to six weeks in length. Satisfactory verification was obtained. Additional refinement of the model could be achieved by increasing the scope of the data input but this does not appear to be justified at the present time. (Author)