During postulated severe accidents in nuclear power plants, steel sheets and shells may suffer high plastic strains up to several percent. In contrast, for design-basis accidents the strains are within lower limits of the order of 0.2% required by the given rules. In both cases the margins up to structural fracture are of vital interest. In sheets and shells these margins may be reduced by diffuse as well as localized necking. Therefore, this paper investigates the remaining structural deformability described by the uniform elongation strain, where diffuse necking starts, and the quasi-uniform elongation strain, where localized necking starts. The theoretical models developed recently for thin sheets under uniaxial loading are extended to account for biaxial loading. Major findings are confirmed by appropriate structural experiments. Based on these results and their scatter, strain limits are recommended for steel sheets and shells under accident loading, such that fracture can be excluded. The strains caused by the accidents discussed in this paper turn out to be below these limits.