Abstarct: Abstract In this thesis, dynamic crack growth in orthotropic materials subjected to thermal shock is investigated. To achieve this goal, the eXtended Finite Element Method (XFEM) is used to model an orthotropic plate with a predefined crack. A thermal shock is applied to this plate baxsed on the Lord-Shulman (LS) and Green-Naghdi (GN) generalized thermoelasticity models, in which the characteristics of each of them are described in accordance with the propagation of thermal waves in an orthotropic medium. Besides, a variety of tip enrichment functions for the displacement and temperature fields are derived relying on the behavior around the tip of a dynamically growing crack in orthotropic materials. Then, by writing the dimensionless form of the governing equations baxsed on generalized thermoelasticity models and discretizing them in the problem domain using the XFEM, the Newmark method is used to solve the system of coupled dynamic equations in the time domain. After that, to calculate the Stress Intensity Factors (SIFs) of the moving crack, the interaction integral method is used, where the formulation is developed for the problems of dynamic crack growth in orthotropic materials. After obtaining the SIFs using the interaction integral method, the modified form of the maximum circumferential stress criterion is used to calculate the crack growth angle, in which the stress fields near the tip of a moving crack are taken into account. In computing the crack propagation speed, the effect of angular fracture toughness in orthotropic materials is considered. Finally, the accuracy of the proposed method is verified in several numerical examples. In addition, the effect of material orientation, thermal shock, and thermoelasticity models are also investigated in detail.