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Temporary storage of solutes in streams is often controlled by flow‐induced uptake in hyporheic zones. This phenomenon accounts for the tails that are generally observed following the passage of a solute pulse, and such exchange is particularly important for the transport of reactive substances that can be subject to various biogeochemical processes in the subsurface. Advective pumping, induced by streamflow over an irregular permeable bed, leads to a distribution of pore water flow paths in the streambed and a corresponding distribution of subsurface solute residence times. This paper describes a modeling framework that couples longitudinal solute transport in streams with solute advection along a continuous distribution of hyporheic flow paths. Moment methods are used to calculate the shape of solute breakthrough curves in the stream based on various representations of hyporheic exchange, including …