KEY WORDS: stress intensity factors, surface cracks, hollow cylinders, finite element method Several numerical solutions to stress intensity factors for various crack configurations and geometries have been published in the literature. For the case of circumferential external surface cracks in hollow cylinders, Mettu, Raju and Forman [21] have presented finite element solution to the stress intensity factors at three aspect ratios (a/c=0.6, 0.8 and 1.0) and three crack depth to thickness ratios (a/t=0.2, 0.5 and 0.8). However, stress intensity factors for the aspect ratios (a/c=0.2, 0.4 and 2.0) and the crack depth to thickness ratios (a/t=0 and 1) were obtained by extrapolation. As a result, accurate assessment of fracture strengths and life prediction of fatigue cracks cannot be achieved by using the extrapolated results. In this thesis, stress intensity factors for two circumferential external surface crack configurations in hollow cylinders are determined, especially for deep cracks (a/t>0.8), by the finite element method. One of the crack configurations is the configuration suggested by Mettu et al. [21]. The other is a newly proposed crack configuration. Three-dimensional linear elastic finite element models were established and analyzed with ABAQUS [24]. The collapsed, 20-noded, singular solid elements [61] were used around the crack front to simulate the stress singularity near the crack tip. The J contour integral method [38] was adopted to determine the stress intensity factors along the crack front. To verify the validity of the stress intensity factors at the deepest point, the limited displacement extrapolation technique [65] was also employed. Stress intensity factors for surface cracks subjected to tension or bending were available for various geometric parameters such as internal radius to thickness ratio (R/t) ranging from 1 to 300, crack aspect ratio (a/c) ranging from 0.2 to 1.0 and crack depth to thickness ratio (a/t) ranging from 0.2 to 0.99. Stress intensity factors at the deepest point determined by the J contour integral method and the limited displacement extrapolation technique were compared. Moreover, stress intensity factors for the two crack configurations were compared with the results of Mettu et al. [21] and BS7910 [23] when the comparisons were possible. Furthermore, distribution of stress intensity factors along the crack front was investigated. Variations of stress intensity factors with geometric parameters for the new crack configuration were also studied. Finally, an equation for stress intensity factors was developed for deep cracks (0.80≤a/t≤0.99). It can be concluded that the stress intensity factors provide new and valuable data, especially for deep cracks, for assessment of fracture strengths and life prediction of fatigue cracks for the crack configurations considered.