Internal Erosion caused within soil structures, such as earth dams and irrigation ponds, lead to the piping failures of the structures. Most of studies on the internal erosion of soils have been experimental and the computational method to analyze the phenomenon is currently limited. The purpose of this study is to propose the numerical method for solving the internal erosion and the transport of eroded soil particles and to verify the applicability of the method. In this paper, three equations concerning the seepage flow, the change of porosity due to internal erosion and the transport of the eroded soil particles are introduced and computationally solved. The equation of the seepage flow is solved with Finite Element Method, and Finite Volume Method is applied to the equation of the transport of the soil particles. It is shown that the numerical approach can reproduce the experimental date of the previous study.