This paper studies the application of an inverse methodology for problem solving in fracture mechanics using the finite element analysis. The method was applied to both detection of subsurface cracks and the study of propagating cracks. The procedure for detection of subsurface cracks uses a first order optimization analysis coupled with a penalty function to solve for the unknown geometric parameters associated with the internal flaw. The objective function is calculated from normalizing the finite element determined displacements by the prescribed ones at some arbitrary points of the damaged component. The technique was also used for determination of the propagating both 1-D and 2-D planar crack growth directions using the well known maximum strain energy release rate criterion. In all cases studied, a good agreement between the theoretical and/or the experimentally observed crack behavior and the developed technique is achieved.