The effects of surface buoyancy flux. atmospheric wind stress and bottom topography on the horizontal and vertical structure of the density and alongshore velocity fields over a continental shelf are investigated within the context of a two-dimensional steady-state model. Using an iterative procedure, similarity solutions are obtained which include the important nonlinear advective effects in the density diffusion equation. In the absence of a wind stress, a reasonable value for the surface buoyancy flux produces alongshore velocities on the order of 20 cm s−1 and an upwelling-like vertical plane circulation. The depth variation across the shelf significantly affects the vertical structure of the density and velocity fields. The introduction of upwelling favorable winds decreases the horizontal density gradient and its associated baroclinic current. A simple physical explanation for this effect, based on heat conservation, is presented.