This article presents analytical and computational methods for mixed-mode fracture analysis of an orthotropic functionally graded material (FGM) coating-bond coat-substrate structure. The analytical solution is developed by considering an embedded crack in the orthotropic FGM coating. The embedded crack is assumed to be loaded through arbitrary self-equilibrating mixed-mode tractions that are applied to its surfaces. Governing partial differential equations for each of the layers in the trilayer structure are derived in terms of the effective parameters of plane orthotropic elasticity. The problem is then reduced to a system of two singular integral equations, which is solved numerically to evaluate the mixed-mode crack tip parameters. The computational approach is based on the finite element method and is developed by applying the displacement correlation technique. The use of two separate methods in the analyses allowed direct comparisons of the results obtained for an embedded crack in the orthotropic FGM coating, leading to a highly accurate numerical predictive capability. The finite element based approach is used to generate further numerical results by considering periodic cracking in the orthotropic FGM coating. Parametric analyses presented in this article illustrate the influences of the material nonhomogeneity and orthotropy constants, the bond coat thickness, and the crack periodicity on the mixed-mode stress intensity factors and the energy release rate.