Analysis of an external semi-elliptical circumferential surface crack in hollow cylinders is practically important in order to evaluate the static or fatigue strength of pressure vessels or pipings. However there are few papers which treated this problem. In this paper, the accurate values of stress intensity factor for this problem are calculated by the body force method. The differences between the stress intensity factor for this problem and that for a semi-elliptical surface crack in a plate are discussed. According to these results, the stress intensity factors for a semi-elliptical surface crack in a hollow cylinder can be approximated by those for a semi-elliptical surface crack in a plate within about 3% in the case when t/<Ri>≤0.4, 0.5≤b/a≤1.0 and b/t≤0.6. The stress intensity factors for a semi-elliptical surface crack in a shaft were also calculated in order to check the accuracy of this method. Their approximate expressions, effective for practical application, are shown.