A practical approach to modeling the hydraulic interaction of a stream and aquifer via streambed leakage is based on the established U.S. Geological Survey (USGS) model, MODFLOW. To represent flood-wave propagation and the associated bank storage, MODFLOW's STREAM module is replaced by the Muskingum-Cunge diffusive-wave-routing scheme. The diffusive wave model closely approximates a dynamic model of a flood wave's speed, shape, and streambed leakage. Because the stream responds more rapidly to disturbances than the aquifer, streambed leakage is calculated at the flood routing time scale in order to properly represent the stream-aquifer coupling. However, both the relative magnitude and timing of aquifer response to a flood wave depend on the strength of this coupling. We find discrepancies in both the flood wave and the streambed leakage when the wave and ground-water motions are evaluated at different time scales. These discrepancies are significant in the case of a strong stream-aquifer coupling, for which equal aquifer and flood-routing time steps may be required. Wave diffusion and bank storage are shown to be comparable in magnitude and should, therefore, be included in stream-aquifer interaction models. Diffusive wave routing more accurately represents wave propagation, bed leakage, and aquifer response if short aquifer time steps are taken, and is preferable to the STREAM module for simulating short time transients. However, the STREAM module is useful for simulating large time frames if accurate modeling of the flood-wave propagation is not required.