A linear, three-dimensional, continuously stratified model is used to study wind-driven ocean circulation near an eastern coast in the presence of a continental shelf. A simplifying assumption is that the alongshore flow field is in geostrophic balance. This assumption allows steady solutions to be obtained numerically with a very efficient scheme. As a result, it is possible to find solutions for a wide variety of model parameters and shelf profiles.A band of equatorward wind forces the ocean, and the resulting solutions have many features in common with observations at eastern boundaries. They all have a surface equatorward jet, but do not always have a coastal undercurrent. When the shelf depth is sufficiently shallow or vertical mixing is sufficiently strong, the speed of the undercurrent, if it exists, is usually weak; in that case, only when there is positive wind curl near the coast does its speed reach commonly observed values. Solutions are sensitive to the choice of bottom topographic profile. A general result is that the continental shelf always acts to strengthen the equatorward jet and to weaken or eliminate the undercurrent. The reason is that the shelf induces an equatorward barotropic component to the shelf currents, a component that is not present in flat-bottom solutions.