This study is concerned with the determination of the rupture conditions of a part-through crack in a relatively thin plate or tube. Zones at the bottom of the crack and at the crack-tip, which have become plastically deformed are replaced by equivalent constraining efforts exerted on the rest of the structure that is assumed to deform elastically. A subsequent elastic analysis, utilizing conformal mapping in which the appropriate boundary conditions are introduced, allows one to determine the aperture at the center of the crack. Two rupture criteria are considered. First, the stress in the connecting ligament at the center of the crack is equal to the rupture stress of the material. Second, the opening at the center of the crack is a critical material characteristic. Experimental verifications were conducted on A106B steel and on AISI 304 steel at 540°C which predicted the point of bursting of tubes within 15% and 10% respectively in 90% of the cases.