An approximate theory of vibrations of orthotropic, thick, cylindrical shells, in which the effect of transverse normal stress is retained, is deduced from the three‐dimensional theory of elasticity. The present theory contains, in addition to the usual membrane and bending terms, the influence of rotatory inertia and transverse‐shear deformation. As an application, the propagation of free harmonic waves in an infinite cylindrical shell is studied. Numerical results are given for relatively thin and thick shells of isotropic and nonisotropic materials.