Abstract: In this paper, the plane elasticity problem for afunctionally graded coating containing a crack bonded to homogeneousmaterial substrate is studied. It is assumed that in the coating,the reciprocal of the shear modulus is a linear function of the coordinate,while Poisson's ratio keeps constant. By utilizing the Fouriertransformation technique and the transfer matrix method, the mixed boundaryproblem is reduced to a system of singular integral equations, which aresolved numerically. The influences of the geometric parameters and thegraded parameter on the stress intensity factors are investigated. Thenumerical results show that the graded parameters, the thickness of coating,and the crack size have significant effects on the stress intensity factors.