The flow of liquids through porous media is treated as a generalized case of Darcy’s Law by dividing the body into finite elements and satisfying continuity of flow and pressure equilibrium from element to element. This technique is applied to flow problems where a free-surface exists and a systematic variational method for describing this surface is developed. The material permeability may be described by a non-isotropic, space varying, second rank tensor. The class of solutions is restricted to two dimensional problems and examples for plane conditions and axial symmetry are given.