Abstract: Along with the vigorous developing construction,the number of various underground engineerings is greatly increasing,such as the foundations of dams and high-rise dmultistored hauses,the subways and the tunnels,the water and oil wells etc.,where the close attention is always paid to the seepage behaviour in the media around the structures.In Appl.Math Mech.1996,17(6),the variational inequality formulation and its FEM solution for the free boundary problem of 2D steady state seepage flow was given by She Yinghe et al.In this paper a further investigation is made on the non-steady state seepage problem,by taking the seepage flow of wells as an example.The presented approach——variational inequality and its FEM solution——is also very beneficial to the non-steady state problems,where the transient free boundary can also be defined directly without conventional iterations.