To prevent undue radio interference and energy loss from overhead conductors, the permissible operating stress must be minimised. Therefore, the design of such conductors was investigated theoretically using a conformal transformation proposed by Timascheff. First, the effect of the design parameters, that is, the subconductor diameter, subconductor spacing, number of subconductors and phase spacing on the maximum surface stress, was considered. This showed that the surface stress decreases as the subconductor diameter, number of subconductors and phase spacing is increased. It also showed that there is an optimum subconductor spacing at which the surface stress is a minimum. Secondly, an equation defining the optimum subconductor spacing was determined. From this equation, it was found that the optimum spacing is affected by all the other parameters, and that subconductor spacings close to the optimum can be justified economically. Finally, the general design of conductor systems was discussed, and possible conductors for a 765kV system were computed using optimum spacings. This showed that the total conductor material is considerably reduced and that the overall diameter of the bundle remains unchanged with an increasing number of subconductors. A suggested computational method for determining possible conductor systems was also described.