The results of an investigation into the mathematical design, as distinct from analysis, of electrical power-system networks are described.Starting with geographical positions of the substations which it is required to interconnect, it is shown that a set of equations can be obtained which are solvable by linear-programming techniques to obtain a minimum-cost network design. Any security of supply conditions considered necessary can be incorporated into the design equations.Solution of the resulting linear programmes requires the use of a digital computer; the necessary computer size, and amount of computation, increases rapidly with increase in the number of substations to be interconnected. With this in mind, suggestions for increasing the size of problem solvable on a given computer are made.Three designs have been completed using the method proposed. These and the results of network-analyser studies on two of them are summarized.The equations for two other possible network-design criteria, minimum circuit length and minimum apparent-power by distance product, are also given and briefly commented upon.