The finite element method has become established as a powerful tool for the solution of many problems of continuum mechanics where its physical interpretation, by analogy with discrete problems of structural analysis permits the user to exercise a considerable degree of insight and judgement in its use. Further it is now a recognized mathematical procedure of approximation which embraces many older methodologies (such as the finite difference method) as a subclass. In the field of geological studies its impact is fairly recent and only a limited application has been made to date. The techniques used here have been limited to those established over a decade ago in the parallel fields and recent developments and possibilities barely touched upon. In this paper the author therefore attempts to (a) outline some of the general mathematical and practical aspects of the method with illustrations from various fields which are relevant to geological problems, (b) survey accomplishments already made in geology and geotechnical fields, and (c) suggest some possible new extensions of application.