The axisymmetric and non-symmetric vibrations of spherical shells are analysed using the thick shell theory. The semi-analytical method is used to reduce the dimension of the problem. A thick shell finite element is developed for the analysis of general shells of revolution and used for this purpose. The element can be used for the analysis of thick and thin shells of revolution. Effects of transverse shear, normal strain and rotary inertia are included in the formulation. Both shallow and deep shells are considered for the analysis. Frequencies are obtained for spherical caps with and without centre cutout. © 1992.