Abstarct: In this thesis, the stress intensity factor for a semi-elliptical/circumferential crack in a thick-walled plate/cylinder which is made of homogenous and isotropic materials and subjected to the non-Fourier (hyperbolic) thermal shock is derived analytically and numerically. The uncoupled thermoelasticity governing equations are assumed. The non-dimensional hyperbolic heat equation is solved using Finite Hankel Transform and separation of variables method. The weight function method is implemented to obtain the stress intensity factor for the deepest and surface points the crack. Results show the different behavior of the crack under hyperbolic thermal shock. At a short time after the thermal shock, the stress intensity factor at the deepest point of the semi-elliptical crack –especially for shallow cracks- for hyperbolic model is significantly greater than Fourier one. The stress intensity factor at the deepest point is greater as the crack is narrower for both models. Unlike mechanical loading, the maximum stress intensity factor may occur at the surface point. For relatively short circumferential cracks, the maximum stress intensity factor of Fourier and hyperbolic models is closed. But for longer cracks, the stress intensity factor of the hyperbolic model is significantly greater than Fourier model. Moreover, the maximum stress intensity factor in hyperbolic model occurs for a crack the peak of stress wave reaches to its tip. According to the results, selection of adequate heat conduction model for structure design under transient thermal loading is critical.