The classical one-dimensional advection-diffusion equation (ADE) gives an inadequate description of tracer cloud evolution in the River Severn, U.K. A solute transport model incorporating the effects of tracer storage in dead zones is presented in which the channel is conceived as being divided into two parallel regions. The bulk flow region occurs in the central part. Its longitudinal dispersive properties are described by the ADE. Adjacent to this, an additional cross-sectional area is defined in which tracer can be stored temporarily in regions of slowly moving water called dead zones. Exchange between the two regions follows a first order rate equation. Applying the model to the River Severn shows that a dispersing cloud’s evolution occurs in two distinct stages with a rapid transitional phase. Initially, shear-dispersion is dominant while the tracer particles mix fully over the bulk flow. Once this has occurred, dead zone storage accounts well for the non-Fickian evolution of the cloud. After the transitional phase the dead zone storage mechanism clearly dominates over shear-dispersion. Overall, the combined shear flow dispersion – dead zone model (D-DZM) provides a much better, physically consistent description of the tracer cloud’s evolution than the simple classical ADE approach can do alone.