In this paper the transient thermal stress problem for a hollow elastic cylinder containing an internal circumferential edge crack is considered. It is assumed that the problem is axisymmetric with regard to the crack geometry and the loading, and that the inertia effects are negligible. The problem is solved for a cylinder that is suddenly cooled from inside. First the transient temperature and stress distributions in an uncracked cylinder are calculated. By using the equal and opposite of this thermal stress as the crack surface traction in the isothermal cylinder the crack problem is then solved and the stress intensity factor is calculated. The numerical results are obtained as a function of the Fourier number tD//b2representing the time for various inner-to-outer radius ratios and relative crack depths, where D and b are respectively the coefficient of diffusivity and the outer radius of the cylinder.