Abstract: External circumferential surface crack was one of the common defects in submarine pipes and risers. For the sake of accurate and efficient calculation of stress intensity factors (SIFs), a two-dimensional weight function for external circumferential surface cracks in cylinders under arbitrary complex stress fields was proposed. Three-dimensional finite element analysis was utilized to calculate the SIFs for external circumferential surface cracks in cylinders under uniform stress loading, covering the thickness-to-radius ratio T/R_i of 0.02 ~ 0.2, crack shape ratio a/c of 0.2 ~ 1.0, and crack depth ratio a/T of 0.1 ~ 0.8. The two-dimensional weight functions for the deepest and surface points of surface cracks were derived. The results of the weight function method and the finite element method were compared to verify the accuracy of the weight function by calculating the SIF under high-order stress loads. The maximum relative error of the two methods was 9.5%. Moreover, the SIFs of external circumferential surface cracks under girth-welded residual stress was calculated. The relative error between the weight function and the finite element results was less than 5%. The results showed that the developed two-dimensional weight function can provide a foundation for the fatigue life prediction of submarine pipes and risers with external circumferential surface cracks.