The influence of submarine canyons on shelf currents is studied using the Rossby adjustment method for a homogeneous, inviscid fluid on an f plane. The canyon in the model is assumed to have vertical edges and constant width. The geostrophic flow around a canyon is found to be dependent upon two geometric parameters: the ratio of the depth of the canyon to the depth of the shelf and the ratio of the width of the canyon to the Rossby radius over the canyon. Moreover, a single parameter determines most of the properties of the geostrophic state. This parameter is called the canyon number and is a combination of the two basic geometric parameters. In the geostrophic state an infinitely long flat-bottom canyon will act as a complete barrier to an approaching shelf flow. The approaching flow is asymmetrically diverted along the canyon, and a net flux is generated to the left of the flow in the northern hemisphere. If the canyon cuts a shelf between the shelf break and the coast and connects to a strait (the geometry of Juan de Fuca Canyon) an in-canyon (out-canyon) current will be generated when the shelf break current flows keeping the shelf at its left (right) in the northern hemisphere. If the canyon has a stepped or sloped bottom, the geostrophic flow has a singularity where the step or slope meets the left canyon edge (looking upcanyon) in the northern hemisphere. Flow can cross the canyon edge through the singularity, so the canyon is no longer a complete barrier to the approaching shelf flow. In this case, as above, a net flux is generated to the left of the approaching shelf flow. ¿ American Geophysical Union 1996