An external axial surface flaw in a metallic round pipe subjected to an internal pressure or various types of stress distributions on the crack faces is considered. The longitudinal surface defect is assumed to have an elliptical-arc shape with the ellipse aspect ratio changing during the whole propagation, as has been deduced through several experimental investigations. The ratio R* = R / t between the inner radius and the wall thickness of the pipe is equal to 1 (thick-walled pipe). The stress-intensity factor along the crack front is derived by applying the finite element method. Then a numerical simulation procedure is carried out to predict the crack growth under cyclic internal pressure. Some results are compared to those determined by other authors.