In this paper, we consider the problem of a functionally graded coating bonded to a homogeneous substrate with a partially insulated interface crack subject to both thermal and mechanical loading. The equations of heat conduction and plane elasticity are converted analytically into singular integral equations which are solved numerically to yield the temperature and the displacement fields in the medium as well as the stress intensity factors. The Finite Element Method was also used to model the crack problem and to compute the crack-tip stress intensity factors using higher order nonhomogeneous elements. The main objective of the paper is to study the effect of the material nonhomogeneity parameters on the crack tip stress intensity factors for further understanding the behavior of graded materials.