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SUMMARYIt is always difficult to solve the coupled soil-pore fluid problem when the soil is saturated and impermeable, because this situation often results in intensive oscillations of the solutions. This topic has been discussed widely in the field of the finite element method but rarely by meshless methods. The ElementFree Galerkin (EFG) method has outstanding advantages of solving this problem, based on the fact that its interpolation function can be constructed flexibly by the nodes in the compact domain. In this study, an EFG numerical model together with a stabilization technique is proposed to obtain stable solutions, especially for the saturated and impermeable soil. Close agreement between computational results and analytical solutions for one-and two-dimensional examples shows that the proposed numerical model not only provides highly accurate solutions for the saturated soil with relatively high permeability, but also eliminates the oscillations of the solutions very effectively for the saturated and impermeable soil. Furthermore, the influences of the hydraulic anisotropy, a typical property of two-dimensional problems, on the proposed stabilization technique are discussed. It is suggested that the optimal distribution of the nodes of essential variables can be designed, according to the relative importance of the permeability in different directions.