1. An algorithm was developed for finding the optimal form of concrete arch dams on the basis of using the method of local variations for minimizing the functional of an expanded objective function consisting of the function of the volume of concrete and penalty function taking into account the conditions of the strength of the material and structural constraints. 2. On the basis of the algorithm developed, a universal software package OPTAR was created for solving problems of optimizing concrete arch dams, making it possible to obtain an accuracy acceptable from the engineering viewpoint with moderate expenditures of computer time. 3. The problem of optimizing a concrete arch dam at a rectangular site was solved by means of the aforementioned software package. The results of the optimization calculation make it possible to reduce the volume of concrete by 40% in comparison with the initial design. 4. The optimal design obtained is markedly underloaded with respect to compression. The tensile stresses at the root of the crown cantilever on the upstream face are the main limiting factor. On the basis of this, it is expedient to use zoning of concrete and to consider the possibility of increasing the degree of use of the concrete strength by using dam designs with various joints increasing the radial displacements of the dam crest and reducing the concentration of cantilever stresses. 5. For a more complete testing of the proposed method, it is necessary to carry out further optimization investigations of arch dams for which there are already optimal solutions obtained by other methods, as well as for dams whose designs were developed on the basis of traditional variant designing.