Mechanical models are used to investigate the formation of accretionary prisms and related basins fed by sediments supplied from adjacent continents and subjected to sediment subduction. Results show that prisms forming under the influence of a hinterland sediment flux exhibit markedly different characteristics compared to classic critical wedges with identical mechanical properties forming by frontal accretion of a preexisting layer. The main differences are reduced surface slopes, increased spacing between thrusts, widespread wedge-top basins, and the presence of buried structures. These differences are explained by the ability of continuous sedimentation to reduce differential stresses in the wedge, leading to stable (supercritical) geometries. Thus, in regions of active sedimentation, wedge geometries cannot be explained solely in terms of relative strengths of the wedge and its décollement, as is the case for critical wedges. Results also show that variations in the relative rates of sediment supply (e.g., linked to climate changes) and sediment subduction may lead to pulsed growth and decline of wedges though time, as has been evidenced for some natural wedges. Thus, rather than viewing compressive plate margins as accretionary versus erosive, the dominant mode may repeatedly switch back and forth through time in response to variations in relative rates of sediment supply and sediment subduction.