Transport of dissolved material in streams and small rivers may be characterized using tracer-dilution methods and solute transport models. Recent studies have quantified stream/substream interactions using models of transient storage. These studies are based on tracer-dilution data obtained during periods of steady flow. We present a modeling framework for the analysis of transient storage in stream systems with unsteady flows. The framework couples a kinematic wave routing model with a solute transport model that includes transient storage. The routing model provides time-varying flows and cross-sectional areas that are used as input to the solute transport model. The modeling framework was used to quantify stream/substream interaction in Huey Creek, an Antarctic stream fed exclusively by glacial meltwater. Analysis of tracer-dilution data indicates that there was substantial interaction between the flowing surface water and the hyporheic (substream) zone. The ratio of storage zone area to stream cross-sectional area (A_s/A) was >1 in all stream reaches, indicating that the substream area contributing to hyporheic exchange was large relative to stream cross-sectional area. The rate of exchange, as governed by the transient storage exchange coefficient (α), was rapid because of a high stream gradient and porous alluvial materials. Estimates of α generally exceed those determined for other small streams. The high degree of hyporheic exchange supports the hypothesis that weathering reactions within the hyporheos account for observed increases in solute concentration with stream length, as noted in other studies of Antarctic streams.