A diffusion (noninertial) hydrodynamic model of coupled two-dimensional overland flow and one-dimensional open-channel flow has been developed. Because the noninertial form of hydrodynamic flow equations is used, several important hydraulic effects that cannot be handled by the kinematic routing techniques--the approach employed in most watershed models--are accommodated in this model; namely, the model is capable of treating such effects as backwater, drawdown, channel overflow, storage and ponding. Although these hydraulic effects were commonly neglected in the past, they are important in drainage studies involving deficiencies of flood control channel and subtle grade differences between alluvial fan watershed boundaries.