The matrix displacement approach of the finite element method is applied to the analysis of deformations and stresses in pressure-vessel type structures. Particular reference is made to structures with rotational symmetry, both under axisymmetric and unsymmetric loading and temperature distribution, for which two classes of structural elements for the idealization of solids and membrane shells are described. A survey of some finite elements used for the analysis of more general pressure vessel structures is conducted. Several examples of axisymmetric and nonsymmetric structures are included to demonstrate the versatility and power of the method.