A simple finite Froude number, quasigeostrophic, frictionless model is developed to study the response of a boundary undercurrent, such as the California Undercurrent, to variations in the underlying topography. Despite its baroclinic nature, the flow tends to follow contours of total depth, although this pattern of response is not fully achieved. Over deep, narrow canyons the flow separates from the bottom. Another simple model containing stratification and frictional effects predicts upwelling to occur in the underlying water within the canyon. ¿ American Geophysical Union 1990