Submarine canyons that cut into the continental shelf are regions of enhanced upwelling. The depth of upwelling and flux through the canyons determines their role in exchange between the shelf and the open ocean. Scaling analyses that relate these quantities to the strength of the flow, stratification, Coriolis parameter, and topographic shape parameters allow their estimation in the absence of a full numerical simulation or a detailed field study. Here we add the effect of the continental shelf slope to the scaling of the depth of upwelling, upwelling flux, and deep water stretching. The scaling is then tested using a three-dimensional primitive equation model over 18 distinct geometries. The impact of the continental shelf is significant for real canyons with changes in the depth of upwelling of up to 11% and of the flux of upwelling of up to 70%. The numerical simulations clearly show three types of canyon upwelling, a symmetric time-dependent flux, the dominant advection-driven flux, and a new flux that appears to be related to internal waves. They also suggest that the canyon width is more important than the upstream canyon shape in determining the strength of the flow across the canyon.