The geostrophic adjustment of a stratified coastal current in the presence of a submarine canyon is considered with a mathematical model in which the vertical structure of the fluid is handled with a ''level'' technique that represents vertical gradients by finite differences. Two situations are investigated in detail: a two-level system where one level represents the shelf and one the canyon, and a three-level system with two levels over the shelf and one in the canyon. There are four important length scales in the adjustment process: the initial width of the coastal current, the width of the canyon, and the internal and external radii of deformation. For each vertical mode, the shorter of the radius of deformation for that mode and the width of the coastal current determines the distance over which the perturbing influence of the canyon decays. For typical shelf situations, the external mode decays with the width of the coastal current, while the internal modes decay with the internal radius of deformation. The width of the canyon determines the strength of the cross-canyon flow and thus, the strength of the canyon's effect on the overlying coastal current, with the interaction becoming smaller as the canyon width becomes small, the importance of the geostrophic balance decreases and the internal density gradients become more important in balancing pressure gradients. Therefore even in the case of flow over a narrow canyon, the isopycnals at the top of the canyon are distorted and there will be some residual circulation on the shelf that is forced by the presence of the canyon. ¿ American Geophysical Union 1989