Two methods for solving two‐dimensional free‐surface flows in porous media are presented. Both are based on the fact that the free surface can be transformed into a straight line. The first method utilizes the principle of images, whereas in the second method the Schwarz‐Christoffel transformation is used. The solution for free‐surface flow into a sink is given to illustrate the first method. The solution of the problem of water wedging is given to illustrate the second method.