Axisymmetric free vibration of thick orthotropic spherical shells with linearly varying thickness along the meridian is analysed. Both deep and shallow shells are considered for the analysis. The effect of thickness variation and lay-up are considered. The results are presented for clamped and hinged boundary conditions. A thick shell finite element is used for the analysis. It is observed that the thickness variation and lay-up have a pronounced effect on the natural frequencies and a considerable increase of the natural frequencies can be achieved by selecting a proper combination of lay-up and thickness variation. © 1992.