Analytical and computational methods are developed to examine mixed-mode fracture behaviour of an orthotropic FGM coating bonded to a homogeneous substrate through a layer of a bond-coat. The coating is assumed to contain an embedded crack perpendicular to the direction of the material property gradation. First, an analytical solution is developed considering a perturbation problem. Using Fourier transform, the problem is reduced to a system of singular integral equations which are solved by means of an expansion-collocation technique. Then, finite element method is utilized to investigate the same problem using the displacement correlation technique (DCT). By using the developed finite element method, mixed-mode stress intensity factors are also evaluated for an FGM coating-bond coat-substrate structure that is subjected to thermal stresses.