Abstarct: In recent years, functionally graded materials were lionized increasingly by engineers and researchers due to their favorite and controllable mechanical and thermal properties. Functionally graded materials consist of ceramic and mextal components, are the most conventional FGMs which vary gradually from ceramic phase in one side to mextal phase on other side. These materials benefit of high fracture toughness and mechanical strength of mextals and high thermal, corrosion and wear strength of ceramics simultaneously. Crack propagation phenomenon under dynamic loadings due to inherent brittleness of ceramics is important factor in failure of FGMs in many engineering applications. Therefore, the fracture analyses of FGMs under thermo-mechanical shocks are important to their durability in engineering applications. In this thesis, the fracture behavior of functionally graded materials under thermo-mechanical shocks is investigated. For this purpose, classical coupled thermoelastic equations are used in calculations. First, these equations are discretized with extended finite element method in the space domain and then they are solved by the Newmark method in the time domain. In this thesis, micromechanical models for conventional composites with assist of generalized isoparametric element formulation, which continuously models the material properties across the elements, are used to estimate material properties of FG laxyers. The most general form of interaction integral is extracted for moving cracks in FGMs under thermo-mechanical loadings, and then it is employed to calculate the stress intensity factors at each time step. All stages of problem solution from mesh generation to obtaining results were implemented in MATLAB programming environment. Four numerical examples are solved and obtained results are compared with existing analytical and numerical results in literature. Good accordance between these results verifies presented method and written code in this research. Finally, tree numerical examples consist of an Al2O3/Si3N4 FG laxyer with edge crack under thermal shock, a glass/epoxy cracked FG beam under thermo-mechanical shock and a Ti-6Al-4V/ZrO2 FG laxyer with edge crack under thermo-mechanical shock are solved. The effects of material properties variations profile on dynamic stress intensity factors are investigated in these examples. In addition, crack propagation path and speed are studied in these examples.