Circular cylindrical and circular conical composite shells (angle wound) are analysed for their free vibration characteristics using thin (Love's first approximation shell theory without thickness shear and rotatory inertia) and moderately thick shell theory with shear deformation and rotatory inertia. The semi-analytical finite element method is used for the solution. Shells with thin shell theory are solved using a two-noded axisymmetric finite element with 16 degrees of freedom per element. Moderately thick shells are solved using a higher order semi-analytical finite element with three nodes and 30 degrees of freedom per element. The circumferential variation is represented in terms of a double Fourier series in order to incorporate the effect of coupling due to anisotropic properties. Comparison of frequencies of shells using thin and thick shell theories is made to study the effect of transverse shear and rotatory inertia for various values of average thickness to small end radius ratio. A parametric study is made to provide insight into the influence of various geometric and material properties of composite shells. © 1993.