A new finite element method (FEM) in consideration of inhomogeneous stress field is introduced to study the dislocation of a listric normal fault zone's displacement and stress fields. New results reveal: (1) the site of maximum slip is at the middle part of the fault, not near the surface. (2) the maximum horizontal and vertical displacements at the ground surface are located at some distance from the fault trace. (3) slip of the fault may result in two failure regions near the ground surface: one close to the surface trace of the fault, and the other within the hanging wall at some distance from the fault; it is in the regions that a succession of normal faults is typically observed in geological examples. 4) The maximum shear stress drop of the fault is also at its middle part.