The variation of Biochemical Oxygen Demand (BOD) and Dissolved Oxygen (DO) along a stretch of a polluted natural stream can be represented by two second-order partial differential equations. These equations are similar to the equation representing the conduction of heat in solids, with the exception that the stream equations contain additional lower order terms. Analytical solutions have been obtained for many cases of the heat-conduction problem. However, the presence of the lower order terms and the complexities of many of the boundary conditions make it impossible to obtain analytical solutions to the BOD and DO profile equations for most cases of practical interest. Furthermore, the numerical procedures which have been found to work for the solution of the heat conduction equation are not satisfactory for the BOD and DO equations because of the effects introduced by the lower-order terms. Procedures are presented for the numerical solution of the BOD and DO equations under temporally and spatially varying BOD and DO inputs. The procedures described are confined to the condition of steady, uniform stream flow.