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Hollow circular cylinders are widely used as pressure vessels, for example, in the nuclear and chemical industries. In this study, stress intensity factors for axial cracks in hollow cylinders subjected to thermal shock are determined by using the thermal weight function method. The thermal weight function is a universal function for a given cracked body and can be obtained from any arbitrary mechanical loading system. The thermal weight function may be though of as Green`s function for the stress intensity factor of cracked bodies subject to thermal loadings. Once the thermal weight function for a cracked body is determined, the stress intensity factor for any arbitrary distributed thermal loading can be simply and efficiently evaluated through the integration of the product of the temperature and the correspondent thermal weight function. A numerical boundary element method for the determination of thermal weight functions for axial cracks in hollow cylinders is used in this study to evaluate the transient stress intensity factor. As a demonstration, some examples of axial cracks in hollow cylinders subjected to thermal shock are solved by using the thermal weight function method, and the results are compared with available results in the published literature.