Abstract: The perturbation theoryis used to solve a nonlinear fluid-solid couplingseepage flow problem, where a small parameter is introduced. A numerical example is given to analyze the pore pressurealong the horizontal distance at different saturation s and time t.The theoreticalevidence is provided for the relation ofpressure-saturation-permeability. Furthermore, a reliable analysis method isoffered to solve the nonlinear partial differential equations.