Nearly all successions of near-shore strata exhibit cyclical movements of the shoreline, which have commonly been attributed to cyclical oscillations in relative sea level (combining eustasy and subsidence) or, more rarely, to cyclical variations in sediment supply. It has become accepted that cyclical change in sediment delivery from source catchments may lead to cyclical movement of boundaries such as the gravel front, particularly in the proximal segments of sediment routing systems. In order to quantitatively assess how variations in sediment transport as a consequence of change in relative sea-level and surface run-off control stratigraphic architecture, we develop a simple numerical model of sediment transport and explore the sensitivity of moving boundaries within the sediment routing system to change in upstream (sediment flux, precipitation rate) and downstream (sea level) controls. We find that downstream controls impact the shoreline and sand front, while the upstream controls can impact the whole system depending on the amplitude of change in sediment flux and precipitation rate. The model implies that under certain conditions the relative movement of the gravel front and shoreline is a diagnostic marker of whether the sediment routing system experienced oscillations in sea level or climatic conditions. The model is then used to assess the controls on stratigraphic architecture in a well-documented palaeo– sediment-routing system in the Late Cretaceous Western Interior Seaway of North America. Model results suggest that significant movement of the gravel front is forced by pronounced (±50%) oscillations in precipitation rate. The absence of such movement in gravel front position in the studied strata implies that time-equivalent movement of the shoreline was driven by relative sea-level change. We suggest that tracking the relative trajectories of internal boundaries such as the gravel front and shoreline is a powerful tool in constraining the interpretation of stratigraphic sequences.