Free torsional oscillation of a split wire of an overhead transmission line is considered. Torsional oscillations of a split wire were calculated based on a non-linear differential equation obtained by the authors using the Bubnov-Galerkin method. Calculated formulas for torsional stiffness of a split wire have been derived. Ratios between the characteristics of torsional and lateral oscillations of a split wire were obtained, which allow optimal selection of parameters of the devices for vibration and oscillation dampening. The results of calculations agree with the experimental data as well as known the theoretical results. Obtained calculation formulas are recommended for use in design of new overhead transmission lines with split wires and reconstruction of lines already in operation.