In this paper, the stress intensity factor for an internal circumferential crack in a thick-walled cylinder has been determined. The cylinder has been subjected to an axisymmetric thermal shock on the outer surface according to the dual phase lag theory. The uncoupled, quasi-stationary thermoelastic governing equations have been assumed. The temperature and stress fields have been solved analytically in the Laplace domain and its Laplace inversion transform has been obtained numerically. Using weight function method, the stress intensity factor for mode-I has been extracted. Temperature, stress and stress intensity factor of hyperbolic and dual phase lag theories have been compared and the effects of heat flux and temperature gradient time relaxations on the temperature, stress and stress intensity factor have been studied. According to the results, the dual phase lag temperature distribution is different in comparison with the Fourier model. Also, the stress intensity factor for dual phase lag model is significant larger than Fourier one. Moreover, the maximum stress intensity factor in dual phase lag model occurs for a crack that the peak of stress wave reaches to its tip. Results show assumption of adequate heat conduction model for structure design under transient thermal loading is critical.