Abstarct: In this thesis, an extended finite element method (XFEM) is used to model a finite orthotropic sheet including cracks in which the crack has been subjected to thermal or mechanical shock. The equations governing the problem in this thesis are solved dynamically by Newmark's method with three non-coupled thermo-elasticity theories, coupled thermo-elasticity theories and Lordshellman's thermoelasticity; In each of these seasons a convergence test is taken to obtain the desired grating. And dynamic stress intensity coefficients were obtained by J integral method. In addition, the variation of fiber angle and its effect on the dynamic stress intensity coefficient have been studied, and it has been shown that with increasing the fiber angle the dynamic stress coefficient of the first and second modes (K1 and K2) is increased. Also in Chapter 5 (analysis by coupled thermoelasticity theory) and 6 (analysis by Lord Shellman's theory of thermoelasticity) by conducting independence test of the path, independent of the path of J integral method is also investigated. Finally, by comparing the results of the fourth, fifth, and sixth chapters (non-coupled thermoelasticity, coupled thermoelasticity and Lordshellman's thermoelasticity), it is concluded that the dynamic stress coefficient of the first mode (K1) in the thermoelasticist temporal theory Coupled and non-coupled thermoelastic theories are maximized.