We discuss a mathematical model for wave and run-up generated submarine landslides in the canyons of the Bay of Naples (Magnaghi-Dohrn canyon system). The morpho-bathymetry and submarine gravity instabilities of such incisions have been investigated through the interpretation of a high resolution DEM. The canyons are located in a sector of the bay where there is a variable interaction of volcanic activity (Phlegrean Fields and Ischia and Procida Islands) with sedimentary processes due to the Sarno-Sebeto rivers. At present the Naples canyon-system is inactive, as is shown by the Holocene sedimentary drapes deposited during the present sea-level highstand, but gravity instabilities occurred in the recent past at the canyons’ heads. In particular the Dohrn Canyon is characterized by a double regressive head, while the Magnaghi Canyon shows a trilobate head, formed by the junction of three main tributary channels and coincident with the retreat of the shelf break around the 140 m isobath. The results of a simulation of failures in the above source areas show that the amplitude of wave run-up, expressed in terms of the sea floor depth percentage, may range up to 2.5 % of the water depth at the sea bottom.