Boundary element methods have recently come to be widely employed for the analysis of porous media because of the reduction of the dimensions and the consequent saving of computer time. However, even if double nodal points are used, it has so far proven difficult to use these methods and achieve a high degree of accuracy in the computation of the potential flux at corners of domains and at seepage points. In order to obtain a flux value having a high degree accuracy, this paper investigates the use of the Laplace equation as the governing equation for the direct solution of the equation for the continuous condition of flux at the seepage point. Finally, several examples of using this method of analysis for transient free surface problems are given.