Abstract: The hollow composite cylinder consisting of an inner orthotropic functionally graded elastic substrate and an outer orthotropic functionally graded elastic layer with cyclically symmetric cracks is considered under an anti-plane shear load. The method of variable separation is employed to reduce this mixed boundary value problem to a Cauchy singular integral equation, which is solved numerically by the Lobatto-Chebyshev quadrature technique, then the numerical results for the stress intensity factor are obtained. The effects of the graded parameters, geometrical and material constants on the stress intensity factors are discussed.