Exact general solutions of the three‐dimensional elasticity equations of motion in polar cylindrical coordinates are written for axisymmetric and antisymmetric axial shear vibrations. The frequency equation follows immediately from the boundary conditions for the problem of the infinitely long, composite cylinder with two concentric circular‐cylindrical layers which are perfectly bonded at their interface. The branches of the frequency equation are plotted and analyzed. The conditions are pointed out under which it is possible to obtain reasonably accurate estimates of the natural frequencies by assuming that the motions of the casing and core are uncoupled.