A method to evaluate the stress intensity factor of a circumferential crack in a finite length cylinder under non-linear radial temperature distribution, considering the effects of various structural parameters such as cylinder length and edge restraint, is shown. The method was derived by combining the simplified methods to evaluate the stress intensity factor for the crack under linear temperature distribution in the radial direction and under non-linear stress distribution on the crack surface, both previously developed by the authors. By applying the solution of transient radial temperature distribution for a cylinder which is suddenly cooled from inside, the maximum transient stress intensity factor of the crack under this temperature change was discussed. The maximum transient stress intensity factor increased and showed a peak as the crack becomes longer. In addition, the stress intensity factor was strongly affected by the cylinder length, and the stress intensity factor for a long cylinder was not necessarily larger than that for a short one.