Hydrodynamic exchange between a stream and its bed plays an important role in solute transport in rivers. Stream-subsurface exchange is known to occur due to several different mechanisms and different approaches have been used to model the resulting solute transport, but there has been little investigation of the ability of the various models to represent specific exchange processes. This work evaluates the ability of the semiempirical transient storage model (TSM) to represent advective hyporheic exchange driven by bed form-induced pore water flows. The TSM is based on the idealized hypothesis that the flux of contaminants is proportional to the difference in concentration between the bed and the stream. To evaluate the ability of this simplified mass transfer relationship to reproduce advective hyporheic exchange, we apply the TSM to data sets for the exchange of conservative solutes with sand beds in laboratory flumes where bed form-induced pumping is the dominant exchange mechanism. The results show that the simplified expressions used in the TSM can represent some but not all aspects of the pumping process. The TSM can represent advective exchange with shallow beds that have a defined exchange layer restricted by the presence of an impermeable boundary. In this case, transient storage parameters can be directly related to the streamflow conditions and the channel geometry. However, the TSM does not do a good job of representing exchange with a relatively deep sediment bed, where flow along different advective paths in the bed yields a wide distribution of exchange timescales.