This paper describes the determination of stress intensity factors (SIFs) of a 3D surface crack in a circular hollow section (CHS) T/Y-joint subjected to three basic loading. In order to achieve the main objective, an automatic finite element (FE) mesh generator is designed whereby the mesh density and element type of the Crack Tube zone can be controlled by the users. Extensive tests are carried out to check the accuracy and to test the convergence of the mesh models. It is found that the generated mesh models are both accurate and robust. Subsequently, a total of 246 cracked CHS T/Y-joints subjected to axial loading; in-plane bending and out-of-plane bending are analysed, and the influencing parameters β, γ, τ, θ, a/t0 and c/a on the SIFs of a 3D surface crack are investigated in this study. The SIFs at the deepest point of a 3D surface crack are also determined using an indirect method incorporated in BS7910. It is found that the later underestimates the SIFs by as much as -36.9% under axial load for crack located at the crown and -32.9% under out-of-plane bending for crack located at the saddle, respectively. Hence, the indirect method is found to be unsafe in estimating the SIFs of a 3D surface crack in CHS T/Y-joints under certain loading conditions and crack location.