In the paper the galloping phenomenon is modelled by self-excited waves travelling along the cable. The critical conditions of air flow and corresponding changes in the lift coefficient are presented. The motion of the cable was described in relation to equilibrium configuration. Since the wavelengths are small with reference to considered distances and additionally the tension and curvature of equilibrium line of the cable are slowly varying functions of the arc co-ordinate, the problems concerning the travelling waves can be solved using the Wentzel-Kramers-Brillouin (WKB) method. Using this method the equations describing wave numbers and amplitudes of waves were derived. The results of the calculations of amplitudes are presented in the form of plots.