Thick layers of porous rock known as sedimentary basins lie underneath many glaciers in Antarctica that flow into the sea. These layers contain large amounts of groundwater, some of which is seawater. We use a mathematical model to predict how groundwater flows through these basins, finding that seawater can become trapped due to changes in the ice sheet over time. We also predict where water flows out of (or into) these basins, and we discuss possible implications for the glacier.