For close proximity flying on the order of 10-100 meters, Coulomb thrusting presents a promising alternative to other methods of propulsion. This clean and fuel-efficient propulsion method is being investigated for use in formation flying and virtual structures. In the latter application, the individual spacecraft assume fixed positions relative to each other through the use of Coulomb forces. In the work presented here, an analytical and numerical analysis is performed on such virtual structures. In the analytical portion, the constant, open-loop charges necessary to maintain a Hill-frame-static formation are determined for the cases of linear two- and three-spacecraft formations and for the case of equilateral triangular formations with spacecraft of equal mass. In addition, analysis is provided for the N-craft case so that the inter-craft charge products can be determined for any static formation. In the numerical portion, a genetic algorithm is employed to support the analytical results by determining formation geometries and charging schemes such that the formation craft remain static in the Hill frame in the absence of perturbation. The results of the numerical analysis include examples of static two-craft through nine-craft formations, including several formations that display a broader range of configurations than considered in previous works. Issues encountered during the numerical analysis are discussed, as well as the course of action taken to overcome these issues. Finally, a method is presented by which the genetic algorithm could be extended to take advantage of cluster computing.