By using analytical methods, successive restrictions were imposed on a mathematical version of the U. S. Weather Bureau's graphical surface‐runoff model to develop an analytical model that expresses the API‐runoff relations with two equations and five coefficients. The analytical model is similar in concept to the graphical model in that both relate rainfall, week number, and the API measure to surface runoff. The concise relations of the analytical model, however, can be rapidly derived from a historical storm list by computer. When tested, runoff relations, derived with the analytical model over selected watersheds, predicted surface runoff from those watersheds somewhat better than the regional, graphical relations developed for the Val