Summary: Water-coning occurs when bottom-waters enter oil-producing wells, a phenomenon that is often associated with high production rates. A simplified model of water-coning is developed by considering a three- dimensional sink, representing the oil well, above the unknown oil-water interface. Predictions of the interface shape are obtained by using (a) a small parameter expansion in terms of a suction parameter F, (b) a modified approximate method based on the ideas of Muskat and (c) a boundary integral method. It is found that solutions exist only for \(F\leq F_ c\); at the critical value of the suction parameter \(F_ c\), the interface has a cuspoid shape. In physical terms this may be interpreted as a maximum pumping rate for a stable interface, otherwise water will enter the oil well.