Summary: The problem of a shallow shell containing a surface crack and subjected to general loading conditions is considered. It is shown that, as in the three-dimensional elasticity formulation, the mode I state can be separated whereas modes II and III remain coupled. A line spring model is developed to formulate the part-through crack problem under mixed-mode conditions. A shallow shell of arbitrary curvature having a part-through crack located on the outer or the inner surface of the shell is then considered. Reissner’s transverse shear theory is used to formulate the problem by assuming that the shell is subjected to all five moment and stress resultants. The uncoupled antisymmetric problem is solved for cylindrical and toroidal shells having a surface crack in various orientations and the primary and the secondary stress intensity factors are given. The results show that, unlike the through crack problems, in surface cracks the effect of shell curvature on the stress intensity factors is relatively insignificant.