For two dimensional problems such as a through thickness crack, reliable solutions for stress intensity factor have been reported by many literatures. However, in practice, the common flaws in many structural members are surface cracks which may propagate to part through cracks under repeated loading. These two categories of crack are three dimensional. Exact solution of stress intensity factors for these cracks is not available due to the complexity of the problem itself. Reliable computational solutions for stress intensity factors of surface cracks have been reported. However, all serious solutions have a limited range of validity for the crack depth and crack length. For the part through crack no solutions have been found in the literature. For investigating the detailed process of crack growth from surface crack to part through crack, solutions for stress intensity factor are necessary. For cylindrical structural components, surface flaws can appear as internal or external semi-elliptical cracks, in the axial or circumferential direction. The form of flaw being studied in the current work is an internal circumferential semi-elliptical surface crack in a tubular member. Resulting from improper welding, this kind of surface crack can occur in tubes, pipes and pressure vessels. To assess the structural integrity and to predict the fracture strength of such components, determination of the stress intensity factor is one of the most vital factors. In this thesis, stress intensity factors for a wide range of long-deep circumferential semi-elliptical internal surface cracks in tubular members are presented. The crack configurations in the tubular members are subjected to axial tension loading and the stress intensity factors (SIFs) were analyzed by considering the following three main parameters: (1) the crack depth to thickness ratio (a/T), (2) the outer radius to thickness ratio (R/T) and (3) the crack length to tube circumference ratio (c/R). For a/T < 0.8, current finite element results compared well with the results reported in literatures. In order to investigate the detailed process of crack growth from surface crack to part through crack, it is necessary to have the accurate SIF for the a/T > 0.8. Therefore, current finite element analysis was extended to investigate the SIFs by including a wider range of a/T ratio up to 0.99. Finite element analyses of cracked tubes have also been carried out to determine the stress intensity factors along the semi-elliptical crack fronts of part through thickness cracks and through thickness cracks. The range of the crack geometries covered in this study has not been reported previously in the literatures. The relationships between the stress intensity factors and the crack configurations such as crack depth ratio and aspect ratio and the size of the tube have been established. In order to examine the effect of material plasticity on the effect of crack tip deformation of long-deep circumferential semi-elliptical internal surface cracks in tubular members, non-linear finite element analyses were carried out to study the crack deformation as well as the corresponding J-integral value of tubular members with long-deep circumferential semi-elliptical internal surface cracks. Then neural network of MATLAB was used to process those finite element analysis results and suitable equations for predicting the SIFs were proposed.