General modeling concepts and the computational capabilities of a large digital computer were used to describe the detailed physical processes occurring within the boundaries of a watershed which in turn could then more precisely characterize the behavior of an entire watershed. It was assumed that a watershed was composed of a composite group of essentially independent elements and that the runoff water from one element was the source of inflow to its adjacent elements. Runoff hydrographs for each elemental area were developed and integrated over the entire watershed. Physical process considered in the model included interception, infiltration, depressional storage and surface flow. A FORTRAN IV program of the mathematical watershed model is included in the report. The model as given is not considered to be in the finished form, but a refinement of the equations governing the component hydrologic relationships is still needed. This applied particularly to the infiltration and surface runoff processes. (WRSIC abstract)