As a result of advances in high speed digital computers, considerable interest has been shown in the use of a numerical solution of the complete equations of free surface flow to synthesize the unsteady channel and overland flow conditions that occur during a period of runoff. The advantage of this approach is that it provides a logical description of the phenomenon of local inflows entering along a stream flowing at either subcritical or supercritical velocities. This paper shows the feasibility of the approach by comparing the hydrographs and water surface profiles obtained from a numerical solution of the equations with those produced by introducing time varied and spatially varied lateral inflows along the length of a 72‐foot‐long experimental flume. One of the practical problems found with the numerical technique was a sensitivity to errors in the value of the Manningnused to describe the channel roughness. The difficulties imposed by this sensitivity are discussed and compared with the problems associated with traditional routing methods. (Key words: Flood routing; hydraulics; computers, digital; synthes