Abstract: Weight function method to calculate stress intensity factor of thin pipelines with longitudinal internal/external semi-elliptical surface cracks and with a ratio of internal radius to thickness of 10 is stated in this paper. According to related documents, analytical expression of weight functions for the deepest point and the surface point of surface crack is presented. The emphasis is placed on the analysis of relation between the stress intensity factors of the deepest/surface point and the crack deepth a/t and the aspect ratios a/c, under the thermal stress. Some meaningful conclusions are obtained.