A simple theoretical model is developed to describe the steady flow of an estuary onto an adjacent continental shelf. A two-layer density stratification is assumed for the shelf water, and the fluid motion is driven by the positive (upper layer) and negative (lower layer) mass fluxes associated with a pair of point sources located at the mouth of the estuary. The dynamics are linear and include the effects of Coriolis acceleration, turbulent friction, and bottom topography. Analytic solutions for the one-layer single-source problem are found for two special depth profiles. A boundary layer solution is found for the power law depth profile h (y) =αyk, and a global solution is found for the log law profile h (y) =H0<1+α ln(y/Lb)> for small α≪1. Both solutions indicate that the far-field flow is asymmetrically concentrated toward the right-hand coast in the northern hemisphere, a consequence of the basic balance between topographic vortex stretching and bottom friction. This mechanism also applies when a constant alongshore current is present. In the two-layer case the flow in the upper layer generally tends to be concentrated toward the left-hand coast, since the upper fluid feels (1) the interface and not the bottom topography and (2) the interfacial drag exerted by the lower fluid toward the right-hand coast. A brief comparison is made between model predictions and observations for the Hudson and Chesapeake Bay estuaries.