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 of 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.