Abstarct: Thermal stress analysis is one of the most important subjects in engineering, since many structures are subjected to elevated temperature. According to numerous studies, the thermal fracture is commonly and complicated failure mode of structures. The main objective of the current study is the evaluation of fracture parameters (stress intensity factors and T stress) for functionally graded materials using element-free Galerkin method. An interaction integral is developed for calculation of thermal fracture parameters. In addition, the J-integral and the displacement correlation technique are implemented. The level set method is used to model the discontinuities of a crack. Furthermore, the crack-tip enrichment facilitates the capture of crack-tip singularities for thermoelastic fields. In linear thermoelastic governing equations, the semi-analytical mode decomposition method which is the convenient technique for thermal shock analysis is used to obtain the transient temperature distribution. The profile of material characteristics are determined by continuous functions such as exponential function as well as micromechanics models. At last, a few parametric analyses are performed to study the influence of material properties on the thermal stress intensity factor.