Derivation of a design hydrograph from rainfall data is a typical problem when dealing with small catchments; in most cases there are no streamflow data available. Numerical solutions of unsteady flow equations are difficult to adopt for flow on natural catchments because of the uncertainity about the initial and boundary conditions. A simplified approach is suggested in which a catchment topography is characterized by a number of planes and channels. Flow over the planes and the channel flow are computed by a numerical solution of the state variable equations of unsteady gradually varied flow. The state variable model of surface flow offers simplicity and calculating speed compared with the numerical solutions of the complete unsteady flow equations, yet it maintains a reasonable approximation of the physical reality. Example problems of the use of the model in derivation of a design hydrograph for a small catchment, using rainfall intensities and durations as inputs, are presented. The computer program is provided at a nominal charge from the Depository of Unpublished Data, CISTI, National Research Council of Canada, Ottawa, Canada K1A 0S2.