Predicting the lifespan of overhead power conductors is one of the major challenges of the energy sector as it would allow the implementation of more relevant asset management strategies. In this context, wind loadings are particularly studied. Indeed, wind-induced oscillations of the overhead conductors lead to fretting fatigue cycles between the strands that compose it, ultimately provoking the structure ruin as shown in [Said, 2020]. In an effort to predict the lifespan of overhead conductors submitted to this phenomenon, the present work aims to propose a 3D finite element model of a cable where each wire is represented by a beam. Such a model should take into account both frictional contact interactions between the strands composing the cable and geometrical non-linearities resulting from the arbitrary large rotations imposed by wind-induced oscillations. In order to take advantage of the intrinsic small-sliding nature of fretting, frictional contact is modeled by a small-sliding point-wise 2-nodes element between strands of different layers as in [Bussolati, 2020]. This hypothesis considerably shortens needed CPU time while allowing a satisfying precision of the simulation results. The presented work will hence include a 3D exact beam finite element formulation implementation with finite rotations coupled with a point-wise and line-wise small-sliding elements to respectively model both inter-layer and intra-layer frictional contact interactions between strands. Different numerical results and model comparisons will be presented to show the performances and accuracy of the implemented model.