Sequence stratigraphic models predict that during relative sea-level fall, rivers will cut incised valleys across the exposed continental shelf. Incision is driven by the exposure of convex-up topography and consequent downstream increases in stream power. Modern shelf profiles from passive-margin and foreland-basin settings show that profile convexities occur at the shelf edge and at the current highstand coastline (the coastal prism). In nonglacial times, which form much of Earth's history, it is unlikely that the shelf edge was subaerially exposed. During such periods, patterns of incision would have been primarily determined by the shape of the coastal prism. On the basis of modern shelf profiles from passive-margin and foreland-basin settings, river incision of as much as 20 to 70 m would be centered upon the preceding highstand coastline and would be restricted to the inner part of the shelf. Deeper incised valleys would only result from exposure of the shelf edge or from the processes involved in the formation of submarine canyons.