A two-noded finite element is presented for the analysis of thick orthotropic layered shells of revolution based on the discrete layer theory. The effects of transverse shear deformation and rotary inertia are taken into consideration. A piece-wise linear variation of the in-plane displacements across the thickness is assumed. The displacements are expanded in a Fourier series in the circumferential direction, as this reduces the order of the problem facilitating the evaluation of both symmetric and asymmetric circumferential modes of vibration. The effect of piece-wise linear variation on the representation of the shear deformation is studied by means of varying the number of layers across the thickness. The representation and the effect of the boundary conditions are discussed. Results are presented for spherical shells. © 1994 Academic Press Limited.