Subsurface flow within a single riffle of a low-gradient gravel bed stream was modeled in three dimensions using MODFLOW, a finite difference groundwater flow model. Model simulations showed that exchange flows can only occur in this low-gradient, gaining stream because of a zone of alluvial sediment around the stream that has much higher permeability than the surrounding catchment (K = 10-4 m s-1, compared with K = 10-6 to 10-8 m s-1). The key factors controlling exchange flow within the alluvial zone were identified as the hydraulic conductivity of the alluvium, the hydraulic gradient between upstream and downstream ends of the riffle, and the flux of groundwater entering the alluvium from the sides and beneath. In the study riffle each of these factors changes with season, causing a reversal of flow paths in the alluvium and a reduction in exchange flows from about 0.2--0.5 m3 d-1 per meter stream length in summer to about 0.008--0.04 m3 d-1 per meter stream length during fall to spring. The model also revealed that exchange flows are up to twice as strong, but more variable, at the sides of the stream than near the center, and that vertical flow paths beneath the channel are more persistent under the range of conditions modeled than lateral flow paths into the banks.