Abstarct: In this thesis, the extended finite element method (XFEM) is used to model a cracked finite domain in which the surface is subjected to a non-Fourier thermal shock. The dynamic fully coupled thermoelasticity equations baxsed on Lord-Shulman (L-S) theory are considered. The interaction integral is used to extract the stress intensity factors (SIFs). The implicit version of the Newmark scheme is used to solve semidiscrete governing equations. In this research, the effect of relaxation time on the temperature distribution and SIFs under thermal shock is investigated. Also, the time variation of SIFs is investigated in time interval in which the waves pass through the crack tip. The effect of integral domain, mesh sizes and time step on the time variation of SIFs is investigated. Furthermore, secondary heat conduction near the tip of an inclined crack due to the reflection of the thermal wave from its surface and consequently local deviation in temperature and displacement fields is discussed in detail. Also, the time variation of SIF I for stationary and moving cracks under tensile stress wave is compared with available analytical and numerical solutions. Finally, the propagation trajectory and time variation of the tip speed of an edge crack and an inclined crack under classical and L-S thermal shock are investigated.