In this paper a 3D beam-to-beam contact element is presented, to deal with contact problems in the coupled electric - mechanical fields. The beams are supposed to get in contact in a pointwise manner, the detection of the contact points and the computation of all contributions are carried out using a fully symmetric treatment of the two beams. Concerning the mechanical field, Hertz theory of contact for elastic bodies is considered. The contact area is varying according to the beamto- beam angle, being circular only in the case of perpendicular beams. This variation of the shape is taken into account too. The problem is semi-coupled: the mechanical field influences the electric one because of the dependence of the voltage distribution on the contact area.