In this paper, a numerical method is proposed to investigate the propagation of elastic guided waves in the armors protecting cylindrical structures, such as cables and pipes, and evaluate the feasibility of using these waves in the context of non-destructive evaluation and structural health monitoring. Armors usually consist of a large number of helical wires in contact with polymeric sheaths surrounding the structure. The numerical method combines a semi-analytical finite element method written in twisting coordinates, which accounts for the continuous screw symmetry of the problem along the structure axis, with rotational Bloch conditions in the cross-section in order to account for the high order of the discrete circular symmetry. The proposed formulation allows the initial three-dimensional problem to be reduced to a two-dimensional unit cell involving only one wire, well suited for fast computations of contact problems and dispersion curves. The existence of wave modes along the two directions (screw axis and circumferential direction) is justified from a theoretical point of view by considering the metric tensor of a mixed twisting-polar coordinate system. Numerical results are presented for a typical armor of power cable, focusing on longitudinal waves propagating predominantly inside the wires. The internal part of the cable is approximated as a homogenized medium to preserve the continuous screw symmetry of the problem. A comparison with experimental measurements is carried out. The results show that the modal velocity of longitudinal waves behaves as in a single free wire above a limit frequency identified by the model. This is not the case of modal attenuation, always greater in the armor due to mechanical contact with the viscoelastic sheaths. Two modes of potential interest for the non-destructive evaluation of armors are identified. The influence of mechanical contacts on wave propagation in armors is finally discussed, including interwire contact.