This research will address three important problems: (1) the effect of material dissimilarity which occurs with cracks in clad piping and pressure vessels; (2) modeling of small surface flaws in thin-walled components under general loading conditions; and (3) basic micromechanics aspects of fractures produced by flaws at the interface regions in composites. A new analytical method has been developed for solving integral equations, and shows considerable promise in application to the solution of these three problems.