Abstarct: In this thesis, a cracked finite isotropic medium under a non-classic thermal shock is studied. The fully coupled dynamic thermoelasticity equations baxsed on the Green-Naghdi theory of thermoelasticity are considered. The extended finite element method is employed to discrete governing equations in the space, and the Newmark scheme is used as the time integration method. The stress intensity factors, which are extracted using the interaction integral method, are compared with other theories of thermoelasticity. The effect of damping coefficient on the time history of stress intensity factors and temperature field is investigated. Furthermore, the crack tip temperature distribution, which disturbs the temperature distribution, baxsed on the type II and III are compared. The results of a cracked plate under temperature shock demonstrated that the stress intensity factors baxsed on thermoelasticity without energy dissipation were significantly greater than those baxsed on classic and Lord-Shulman models. Whereas, the peak of stress intensity factors under heat flux shock are nearly equal for various theories of thermoelasticity.