Abstarct: In this thesis, the stress intensity factor mode I for an edge-cracked laxyer or an internal semi-elliptical or circumferential crack in an isotropic homogeneous thick-walled cylinder subject to radial thermal shock baxsed on different coupled and uncoupled theories is derived. In the case of uncoupled theories, governing equations are solved analutically in Laplace domain and then a numerical Laplace inversion techniqe is employed to transform the results into the time domain. Also the weight function method is implemented to obtain the stress intensity factor for the circumferential crack, deepest and surface points of the semi-elliptical crack in the cylinder and edge crack in the laxyer. In the case of coupled Chandrasekharaiah-Tzou and Lord-Shulman, governing equations are solved analytically by using Laplace transform and introducing displacement potential function. According to the results, the non-fourier results are different in comparison with Fourier ones. The coupling effect between the thermal and mechanical fields will reduce the thermal wave speed alittle which result in different temperature, stress and stress intensity factor results rather than uncoupled models. Maximum magnitude of temperature, axial and hoop stress baxsed on the generalized theories are higher than the Fourier law and classic theory of thermoelasticity which result in higher stress intensity factor for circumferential, deepest point and surface points of the semi-elliptical cracks for the reason of the heat flux and temperature gradient time relaxations.