The finite element method is extended to the refined elastic analysis of multilayer beams and shells with no restriction placed upon the ratios of the layer thicknesses and properties. The method is applicable to structures wherein shearing deformations are significant, including sandwich-type structures. Element stiffnesses are based on polynomial displacement models and are applicable to the linear elastic analysis of beams and thin, axisymmetric shells of arbitrary meridian. Although attention is restricted to three-layered construction with similar facings, the theory may be generalized to any type of flexural element and any arrangement of laminations. Computer programs have been written for both static analysis and free vibration analysis. Inclusion of rotatory as well as translational inertia allows the determination of natural thickness-shear frequencies and mode shapes in addition to flexural vibration characteristics. Examples are presented to illustrate the effectiveness of the method.