In this study, stress intensity factors for axial cracks in hollow cylinders subjected to mechanical and thermal loadings are determined by using the weight function method. The weight function is a universal function for a given cracked body and can be obtained from any arbitrary loading system. The weight function may be thought of as Green’s function for the stress intensity factor of cracked bodies. Once the weight function for a cracked body is determined, the stress intensity factor for any arbitrary loading can be simply and efficiently evaluated through the integration of the product of the loading and weight function. A numerical method for the determination of weight functions relevant to cracked bodies with finite dimensions is used. Results for weight functions covering a wide range of hollow cylinder geometries are presented in functional or graphical form. The explicit crack face weight functions for applying mechanical loadings are obtained by using the least-squares fitting procedure. As a demonstration, some examples of special loading problems are solved by the weight function method, and the results are compared with available results in the published literature.