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A new finite element method for the seepage in faults or joints of blocky rock mass is presented to match the stability calculation by the block theory. The variational formulation of the finite element method in the continuum medium is modified, and the new method is established. The method is applied to calculate the seepage in rock foundation under an arch dam, and reasonable results are obtained. Because of the same mesh being used, the calculated results of seepage can be directly used to calculate the seepage load for stability calculation without any data transfer.