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The technique of curvilinear boundary-fitted coordinate system is used for the mathematical model of pressure underground seepage flow and the boundary conditions and the method of solving the transformed equations have been presented. The computing example shows that the computed hydraulic parameters conform to the physical laws. Compared with the finite element method, the presented method need not solve the large matrix equations, and the computer memories and the time for computing are less. The mathematical model is effective for numerical solution of pressure underground seepage flows with complicated boundaries, and can be used in practice hydraulic engineering.