A multi-planar tubular KK-joint containing a surface crack is analyzed using finite element method. Five element types are used to model the surface crack to avoid the high aspect ratio of the elements. Both displacement extrapolation method and interaction J-integral method are adopted to calculate the stress intensity factors (SIF) along the crack front, which are usually used to predict the fatigue life for tubular joints in offshore engineering. From the SIF comparison of two methods, the results agree quite well and both methods can be used reliably for analyzing cracked tubular KK-joints. For the parametric study, 70 cracked KK-joint models are analyzed altogether. The results show that the SIFs along a surface crack in a tubular KK-joint under axial loads are mainly determined by joint geometry and crack shape. The values of Y at the deepest point of the surface crack increase as parameters beta, gamma and tau increase, and Y decreases as parameter a/c increases. The values of Y at the crack tips increase as parameters gamma, tau and a/c increase. Conversely, Y decreases as parameters beta and a/T increase.