Abstract: Computer ,and finite-elements method have a very wide range of application in various fields of earth sciences. The results to be obtained from these applications may be of critical importance towards the advancement of ourknowledge of the physical constitution of the earth crust. The purpose of this paper is to introduce to earth scientists thefinite-elements method ,and its application techniques for the solution of various structural problems. In the example givenhere in, the distributions of gravitational ,and tectonic stress components in an elastically heterogeneous material under flatground are shown. From these distributions, the affects of the lithological heterogeneity to the deformation mode of themedium, the points of critical stress concentrations ,and the possible fracture surfaces with their locations ,and directionscould be determined. From the model studies, employing the finite elements method ,and from the computer data, providing that they are interpreted correctly, practical solutions for some structural geology problems could be obtained.