A theoretical and exact solution is presented for steady saturated flow to a fully penetrating well in an elliptical confined aquifer; the aquifer is considered isotropic and homogeneous. The potential and stream functions for a number of different‐shaped aquifers and well locations are developed by starting with a general solution to Laplace's equation and using a modified Gram‐Schmidt method. Flow tables are presented for a number of geometries. For example, the tables show that a well 6 inches in diameter, located in the center of an elliptical aquifer with a ratio of minor to major axis of ½ and a major axis 1000 feet long, provides 0.857 as much discharge as a well located on the major axis of an elliptical aquifer seven‐eighths of the way from the center to the edge. The variety of geometries considered enables one to predict the well discharge for aquifers that approach the shape of an ellipse. Flow net examples are presented.