In this study an unconstrained elastic layer under statically self-equilibrating thermal or residual stresses is considered. The layer is assumed to be a functionally graded material (FGM), meaning that its thermo-mechanical properties are assumed to be continuous functions of the thickness coordinate. The layer contains an embedded or a surface crack perpendicular to its boundaries. Using superposition the problem is reduced to a perturbation problem in which the crack surface tractions are the only external forces. The dimensions, geometry, and loading conditions of the original problem are such that the perturbation problem may be approximated by a plane strain mode I crack problem for an infinite layer. After a general discussion of the thermal stress problem, the crack problem in the nonhomogeneous medium is formulated. With the application to graded coatings and interfacial zones in mind, the thickness variation of the thermo-mechanical properties is assumed to be monotonous. Thus, the functions such as Young's modulus, the thermal expansion coefficient, and thermal conductivity may be expressed by appropriate exponential functions through a two-parameter curve fit. The crack problem is reduced to an integral equation with a generalized Cauchy kernel and solved numerically. After giving some sample results regarding the distribution of thermal stresses, stress intensity factors for embedded and surface cracks are presented. Also included are the results for a crack / contact problem in a FGM layer that is under compression near and at the surface and tension in the interior region.