The stress analysis and fatigue crack growth behaviour of a part-through-cracked double-curvature thin-walled shell is examined. An external surface crack is assumed to lie in one of the principal curvature planes of the shell, and to present a semi-elliptical shape. The stress intensity factors (SIFs) along the crack front for different elementary opening stresses acting on the crack faces are determined through a three-dimensional finite element analysis. Then approximate values of SIF in the case of a cracked pressure vessel are computed by employing the above results together with the superposition principle and the power series expansion of the actual opening stress. Finally, a numerical simulation procedure is carried out to predict the crack growth under cyclic internal pressure. Some results are compared with those of other authors.