The formulation and solution of governing equations that can be used to analyse the three-dimensional behaviour of elastic towing cables subjected to arbitrary sheared currents were presented in this paper. The elastic cable geometry was described in terms of two angles, elevation and azimuth, which are related to Cartesian co-ordinates by geometry compatibility relations. These relations were combined with the cable equilibrium equations to obtain a system of non-linear differential equations. In the end, results for cable tension, angles, geometry and elongation are presented for example cases.