The propagation of elastic surface waves, guided by the free surface of an infinitely long cylinder of arbitrary cross section, is formulated as an eigenvalue problem for an unbounded self-adjoint operator. We prove the existence of a hierarchy of guided modes. Two of them propagate for any value of the wave number, whereas all of the others only exist beyond a cut-off wave number. For any fixed value of the wave number, only a finite number of modes propagate.