In this study, the first mode of stress intensity factor of semi-elliptical circumferential crack in the outer surface of a cylinder with radius to thickness ratio of 30, is investigated. The cylinder is applied in semi-submersible drilling platforms. First, the stress field of the cylinder under thermal and mechanical loads is extracted based on semi couple thermo-elastic equations. Then, the weight functions are derived for deepest and surface points using three reference loads results. Explicit expressions of stress intensity factors for surface and deepest points are presented using thermo-elastic stress field and the weight functions of the cracked cylinder. The results obtained by proposed weight functions and those obtained by finite element method and those presented in the literatures have a good accuracy. The interaction effects of thermal and mechanical loads on the stress intensity factors are studied. The results show that with increasing load ratio, the dimensionless stress intensity factors of deepest and surface points, decrease and increase, respectively.