Abstract: Functionally graded materials (FGMs) have been developed for the needs of the aeronautic and astronautic fields. Due to the reasons of technology, working conditions and some other factors, lots of cracks easily appear in FGMs. Therefore, it is very significant to study the crack problems of FGMs with arbitrarily oriented cracks. In this paper, the FGM with an arbitrarily oriented crack is considered. With the use of integration transform, the displacement form can be obtained. By using auxiliary functions and relative conditions, the present problem is transformed into solving a group of singular integral equations which can be solved numerically by Lobatto-Chebyshev method. Numerical results are obtained to illustrate the variations of the stress intensity factors (SIFs) with the parameters such as nonhomogeneity factor, crack direction and load conditions.