The purpose of this article is to compare two predictive methods of J integral assessments for center-cracked plates, single-edge cracked plates and double-edge cracked plates produced from X52 and X70 steels, and a longitudinally cracked pipe produced from X70 steel. The two methods examined are: the GSM method and the Js procedure of the French RCC-MR construction code, designated here as the FC method. The accuracy of J integral predictions by these methods is visualized by comparing the results obtained with the “reference” values calculated by the EPRI method. The main results showed that both methods yielded similar J integral values, although in most cases, the GSM predictions were slightly more conservative than the FC predictions. In comparison with the “reference” values of the J integral, both methods provided conservative results for most crack configurations, although the estimates for cracks of a relative length smaller than 1/8 were not found to be so conservative. The prediction of burst pressures for external longitudinal semielliptical part-through cracks in X70 steel pipe showed that the magnitudes of predicted burst pressures came very close to each other, and were conservative compared to FEM (finite element method) calculations and experimentally determined burst pressures.