This publication presents the results of an investigation of the elastic-plastic behavior of pressure vessel heads under internal pressure. The work was sponsored over a two-year period by the Pressure Vessel Research Committee with the first year being devoted to ellipsoidal heads and the second year to torispherical heads. Battelle's computer program@ NONLEP@ developed for elastic-plastic analysis of thin shells of revolution@ was applied to a set of typical head geometries subjected to internal pressure. This program includes effects of large deformations and strain hardening and thus it was possible to predict the additional pressure-carrying capability oi heads beyond the collapse pressure predicted by limit analyses. Curves giving details of the numerical results are organized as appendices@ with the main body of the publication devoted to discussion of the analyses.