||In this paper we study numerically the mechanical behaviour of wire ropes, particularly the influence of the geometrical configuration on the overall stiffness of the cables. Modelling the behaviour of a cable is a difficult problem, given the complexity of the geometrical layout, contact phenomena occurring among wires and possible yielding of the material. For this reason we pursue a "hierarchical beam approach", to substitute recursively, at each cabling stage, the bundle of wires with an equivalent single strand, having the characteristics computed from the previous level. We consider the first two levels of the bundle hierarchy and investigate the case of longitudinal stretching, as a representative application of the method for the problem at hand. To this aim, we perform a certain number of numerical experiments on a bundle of wires, by varying their twist pitches. In this way we compose a set of data to train suitable Artificial Neural Networks, so that, given the twist pitches and the applied longitudinal displacement in input, the ANNs give us the longitudinal reaction force, the bundle axial rotation or the overall axial stiffness. These results can be used "directly" to search for geometrical configurations that offer a significant improvement in stiffness, assuming that a higher stiffness will reduce strand bending and wires breakage. Furthermore, they can be used to obtain the characteristics of the single, equivalent beam that we need for our approach.