Coupled circulation between an estuary and the adjacent shelf is a new area of study. At low frequencies estuarine gravitational circulation requires landward flow of lower layer shelf water to balance the seaward flow of brackish estuarine water over the shelf. Here a clearer description of the low frequency physical coupling between the estuary and shelf waters is developed through the use of a steady, linear, barotropic model. Complex bottom topography for the shelf is treated. The shelf adjacent to Delaware Bay, located on the east coast of the United States, is used as an example. The results show that the landward flow field driven only by withdrawal of flow through the estuary's entrance is independent of the flow field otherwise present over the shelf. In the northern hemisphere this landward flow passes along the coast to the right of the estuary entrance, when viewed facing offshore, before it enters the estuary. Model results are supported by near bottom current observations collected on the shelf adjacent to the mouth of Delaware Bay. ¿ American Geophysical Union 1990