The element-free Galerkin method which is en-riched intrinsically is applied for fracture analysis of functionally graded materials under mode I steady-state and transient thermal loading. The stress intensity factors are evaluated by means of both equivalent domain integral and displacement correlation technique. Continuum functions and micromechanical model are used to describe the distri-bution of material properties. For thermal shock analysis, the modal decomposition method which is a semi-discretization approach is implemented to obtain the tran-sient temperature field. The accuracy of numerical results is verified using the available reference solution. The re-sults imply that the magnitude of the stress intensity factor gets to a large peak at the early time of the thermal shock which indicates its significant role in the fracture failure.

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