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An external surface flaw is assumed to be located at the root of a notch ina metallic double-curvature thin-walled shell subjected to an internal pressure. Thisdefect presents an elliptical-arc shape with the ellipse aspect ratio changing during thewhole crack propagation, as has experimentally been observed. An approximateexpression of the stress-intensity factor along the crack front is deduced by applying thefinite element method and the superposition principle. Then a numerical procedure iscarried out to predict the crack growth for cylindrical and spherical shells under cyclicinternal pressure. Some results are compared with those determined by other Authorsfor unnotched shells.