Sediment erosion, transport, and deposition by glaciers and ice sheets play crucial roles in shaping landscapes, provide important nutrients to downstream ecosystems, and preserve key indicators of past climate conditions in the geologic record. While previous work has quantified sediment fluxes from subglacial meltwater, we also observe sediment entrained within basal ice, transported by the flow of the glacier itself. However, the formation and evolution of these debris‐rich ice layers remains poorly understood and rarely represented in landscape evolution models. Here, we identify a characteristic sequence of basal ice layers at Mendenhall Glacier, Alaska. We develop a numerical model of frozen fringe and regelation processes that describes the co‐evolution of this sequence and explore the sensitivity of the model to key properties of the subglacial sedimentary system, using the Instructed Glacier Model to parameterize ice dynamics. Then, we run numerical simulations over the spatial extent of Mendenhall Glacier, showing that the sediment transport model can predict the observed basal ice stratigraphy at the glacier's terminus. From the model results, we estimate basal ice layers transport between 23,300 and 39,800 of sediment, mostly entrained in the lowermost ice layers nearest to the bed, maximized by high effective pressures and slow, convergent flow fields. Overall, our results highlight the role of basal sediment entrainment in delivering eroded material to the glacier terminus and indicate that this process should not be ignored in broader models of landscape evolution.