Environmental and operational conditions cause corrosions and fatigue damage in cables used in civil engineering. For their non-destructive testing, an appropriate method might be to employ guided ultrasonic waves since they can interrogate the entire section of cables for long distances. Cables are typically made of a central wire and several peripheral helical wires. Due to the complexity of such a geometry, only cylindrical waveguides are considered. The present work is dedicated to a numerical study of the interaction of guided waves with non-axisymmetric cracks in an infinite cylinder. The numerical computations are based on a hybrid method involving the Finite Element Method (FEM) and the Semi-Analytical Finite Element (SAFE) technique. The classical FEM is used to analyse the crack and its near field. Then, eigenmode expansions of the solutions at both inlet and outlet cross-sections of the FEM region are performed. The SAFE technique is used to determine the elastic guided modes for both inlet and outlet cross-sections of the volume. The amplitudes of the incident modes are enforced while the amplitudes of the scattered modes are determined by solving the global system of the hybrid FEM-SAFE model. Obtained results for the free-end cylinder compare favourably with results found in the literature. The interaction of the fundamental longitudinal Pochhammer-Chree mode with non-axisymmetric cracks are predicted and discussed.