The influence of an ambient alongshelf current on the formation and offshore transport of dense water from an idealized coastal polynya is examined by using a primitive-equation numerical model. Brine rejection during ice formation within the polynya is modeled by a prescribed surface buoyancy flux over a limited region along a straight coastline. A uniform alongshelf current is imposed at one end of the model domain. The basic ocean response is unchanged by the ambient current; i.e., an unstable density front forms around the polynya perimeter and breaks up into small-scale (15--30 km) eddies that carry the dense water away from the polynya. The ambient current continuously carries water out of the polynya region, thereby both increasing the alongshelf density flux and reducing the typical density anomaly generated. The total volume of dense water formed is not appreciably altered. The influence of a submarine canyon located downstream of the polynya (in the direction of the imposed alongshelf current) is examined. Almost no dense water enters a canyon oriented normally or diagonally to the coast because the ambient flow tends to follow isobaths and carries virtually all of the dense water around and past the canyon. An appreciable fraction of densified water may flow down a canyon oriented parallel to the coast, the details depending on the canyon geometry and the strength of the ambient current. Thus both the density anomalies produced by coastal polynyas and the pathways of dense water transport are sensitive to ambient shelf currents, potentially providing a source of interannual variability in dense water formation and export from the shelf. ¿ 2000 American Geophysical Union