Toroidal shells containing a surface crack and subjected to various sy
mmetric and antisymmetric loading conditions are considered. A singula
r integral formulation of a through crack located along a principal li
ne of curvature of a shell is used along with the line spring model to
treat the surface crack problem. Transverse shear deformations are ta
ken into account in the shell theory. Locating the crack along a line
or principal curvature uncouples the symmetric mode I deformations fro
m the antisymmetric mode II and III deformations, which are inherently
coupled. Mode I loadings considered include membrane loading and bend
ing, while the mode II and III cases include in plane shear, twisting
and transverse shear. In addition to these loadings, residual stresses
resulting in mode I deformations are considered. Stress intensity fac
tors for the various loadings are given for shell geometries represent
ative of spherical caps, cylindrical pipes and pipe elbows for a numbe
r of crack locations.