The stress intensity factors at the deepest point and at the crack ends of a surface crack in a tubular K-joint are calculated by direct and indirect methods. In the direct method, the surface crack is modelled explicitly. An automatic mesh generator is developed to produce a well-graded mesh around the crack region. This is achieved by using five types of elements. Thereafter, the stress intensity factors of a surface crack located anywhere along the weld toe at the joint intersection are calculated using the J-integral method. The computed values had been verified by experimental test results. In the indirect method, the stress intensity factors are estimated by the T-butt solutions used in conjunction with the stress concentration factors (SCFs) and degree of bending (DOB) of the uncracked tubular K-joint. In this study, a total of 1024 models, covering a wide range of geometrical parameters and crack shapes, have been selected and analyzed. Both approaches are able to produce a safe estimation of stress intensity factors at the deepest point of the surface crack. However, the indirect method is found to be extremely conservative; it overestimates the stress intensity factor values by as much as 190.4% (β=0.5, γ=30, τ=0.5, a/T=0.1, c/a=5) at the deepest point, and 390.7% (β=0.4, γ=30, τ=0.5, a/T=0.5, c/a=8) at the crack ends of the surface crack respectively