Stress singularities occur at crack tips, corners and material interfaces. The stress intensity factors and T-stresses are coefficients of structural components where the active stress singular and first regular stress terms, respectively, are denoted by William's eigen function expansion series. A finite element analysis by CASTEM 2000 have been undertaken in order to determine the evolution of the T-stress and stress intensity factor terms in mode I for an arc of pipeline specimens with an external surface crack. A stress difference method described by Moustabchir et al. (2012) are adapted and, in the following step, the volumetric method is then embedded to compute the SIFs and T-stress near the crack tip. Different crack geometries combined with different length-to-thickness ratios are examined for the T-stress and stress-intensity factor. The revisited stress difference method employed here shows to be an accurate and robust scheme for evaluating the T-stress/SIFs in an arc of the pipeline.