This paper deals with the modal analysis of rotational shell structures by means of the
numerical solution technique known as the Generalized Differential Quadrature (G. D. Q.) method. The
treatment is conducted within the Reissner first order shear deformation theory (F. S. D. T.) for linearly
elastic isotropic shells. Starting from a non-linear formulation, the compatibility equations via Principle of
Virtual Works are obtained, for the general shell structure, given the internal equilibrium equations in
terms of stress resultants and couples. These equations are subsequently linearized and specialized for the
rotational geometry, expanding all problem variables in a partial Fourier series, with respect to the
longitudinal coordinate. The procedure leads to the fundamental system of dynamic equilibrium equations
in terms of the reference surface kinematic harmonic components. Finally, a one-dimensional problem, by
means of a set of five ordinary differential equations, in which the only spatial coordinate appearing is the
one along meridians, is obtained. This can be conveniently solved using an appropriate G. D. Q. method
in meridional direction, yielding accurate results with an extremely low computational cost and not using
the so-called “delta-point” technique