A numerical model for an unsaturated flow problem by using finite element method is established in order to simulate liquid moisture flow in an unsaturated zone with homogeneous soil and deep subsurface water, and with different initial and boundary conditions. For infiltration or evaporation problems, a traditional method usually yields oscillatory non-physics profiles. However, we obtain nonoscillatory solutions and evade non-physics solutions for these problems by using the mass-lumped finite element method, Moreover, the kind of boundary conditions is handled very well.