A numerical model has been developed to predict the evolution and degree of incision and deposition by fluvial channels on the continental shelf during sea level cycles. Rainfall-runoff, mass wasting processes, and fluvial sediment entrainment and transport are simulated using the detachment-limited model of Howard <1994> on a grid that represents the morphology of the continental shelf and corresponding coastal plain. The model is coupled with a deltaic module for sediment deposition in the ocean and a fluctuating sea level that mimics climatic changes on a ~104 year timescale. The model indicates that the detailed structure of sea level oscillations has a strong influence upon sediment redistribution and channel development on the shelf. In particular, high-frequency sea level oscillations increase fluvial incision in the terminal reaches of the rivers due to rapid downcutting during the low stands of the oscillation. It is shown that the increment of incision at the river mouth is directly proportional to the oscillation amplitude. Furthermore, simulations indicate that an increase in river sediment load driven by climatic change favors channel avulsion with the formation of new fluvial incisions on the shelf. Results also show the strong influence of shelf morphology on establishing channel networks during sea level low stands.