A three-dimensional method of analysis is presented for determining the free vibration frequencies and mode shapes of hollow bodies of revolution (i.e., thick shells), not limited to straight line generators or constant thickness. The middle surface of the shell nay have arbitrary curvatures, and the wall thickness may vary arbitrarily. Displacement components u_ø, u_z, u_θ in the meridional, normal and circumferential directions, respectively, we taken to be sinusoidal in time, periodic in 0, and a1gebraic polynomials in the f and z directions. Potential(strain) and kinetic energies of the entire body are formulated, and upper bound values of the frequencies are obtained by minimizing the frequencies. As the degrees of the polynomials are increased, frequencies converge to the exact values. Novel numerical results we presented for two types of thick conical shells and thick spherical shell segments having linear thickness variations. Convergence to four digit exactitude is demonstrated for the first five frequencies of both types of shells. The method is applicable to thin shells, as well as thick and very thick ones.