During sea-level low stands continental shelves were dissected by a network of channels somewhat resembling today's coastal plain streams. The network was subsequently buried or erased by marine processes during sea-level transgression, so that only some tracts are still conserved in the geological record. Herein we use a numerical model to study the effect of base level change by sea-level fall on the total channel incision. We find that four factors control the total incision on the shelf: (i) the presence of convex deposits; (ii) the evolution of the rivers towards equilibrium (graded) conditions; (iii) geometrical differences between coastal plain and shelf; and (iv) the exposure of the continental slope. The conceptual model is then applied to the Adriatic Sea, Italy. Simulations show that incisions in the Adriatic shelf develop in high stand fluvial deposits in the early stages of sea-level fall. At lower sea level, fluvial incision occurs in the mid-Adriatic due to the regrading of the Po River after the capture of the Apennine streams in its drainage system.