AbstractA general method is outlined for the determination of natural frequencies of cylindrical shells with any boundary conditions when the effects of rotatory inertia and transverse shear deformation are included in the analysis. This is applied to cylindrical shells with both ends clamped. It is shown that the inclusion of these effects tends to have a greater effect upon frequencies of cylindrical shells with clamped ends than it does for corresponding shells with simply supported ends, for which numerical results are available. The authors suggest an empirical relation, which together with the latter results enables rapid estimates to be made of the effects of rotatory inertia and shear deformation on the frequencies of a wide range of cylindrical shells with clamped ends. An assessment of the accuracy of the theory with these effects included is made by comparing frequencies with values from a three‐dimensional elasticity theory, but this comparison has to be restricted to cylindrical shells with simply supported end