Development of an annular finite element, for the linear elastic analysis of sandwich shells, is reported here. The derivation of stiffness and mass matrices is based on improved shell theory which takes into account the effects of rotary inertia and transverse shear deformation. Flexural rigidity of the faces is included in the formulation. The core of the sandwich shell is assumed to be incompressible in the radial direction. Numerical examples of spherical sandwich shells with two types of boundary conditions—(i) fixed and (ii) pinned along the outer periphery—have been presented. The results are generated for displacements and frequencies.