In this study the axisymmetric crack problem for thermal barrier coatings under a uniform temperature change is considered. Modes I and II stress intensity factors and the strain energy release rate are calculated for various sizes and locations of the crack. The main variables in the problem are the material inhomogeneity parameter of the functionally graded material coating, the size and the location of the crack, and the relative dimensions of the specimen. The effect of the temperature dependence of the material properties on the stress intensity factors and the strain energy release rate is also investigated. The finite element method is used to solve the problem. The material property grading is accounted for by developing special inhomogeneous elements and the stress intensity factors are calculated by using enriched crack tip elements.