The problem considered in this article is the response of a graded composite material plate containing some noncollinear cracks subjected to dynamic thermal loading. It is assumed that all the material properties depend only on the coordinates y (along the thickness direction) . In the analysis, graded regions are treated as a series of perfectly bonded composite layers, each layer being assigned slightly different material properties. Utilizing the Laplace transform and Fourier transform techniques, the general solution for each layer is derived. The complete solution of the entire medium is then obtained by introducing the mechanical boundary and layer interface conditions. The main features of the proposed method are: (1) the material may be orthotropic, (2) multiple crack problem, (3) the material properties may vary arbitrarily along the thickness direction, and (4) with the inertial terms taken into account, the present algorithm can be applied to a fracture problem under dynamic mechanical loading. Numerical examples are provided for a FGM and a substrate FGM coating structure under a nonuniform heating condition. Transient and steady-state thermal stress intensity factors are calculated and their variation due to a change of the material gradient and the location of the crack are studied.