A finite difference approximation to the Love-Meissner equations for the ellipsoidal shell was used to calculate stresses in thin-walled pressure vessels with ellipsoidal heads. Calculations were made with a digital computer for a useful range of the shell parameters. Results are reported in the form of stress indexes and stress intensity indexes, the latter based on the maximum shear theory of failure. Comparisons are made with the available experimental and analytical work in the literature, and stresses are also given for typical heads designed in accordance with the ASME Boiler and Pressure Vessel Code.