AbstractGeneralized applications of modernnumerical analysismethods—while digital computers experienced a fast development—produced a first revolution in design techniques, allowing one to perform computations considered unapproachable until that time. Introduction ofComputer Aided Design(CAD) techniques—while high‐performance graphic peripherals experience a fast development—is actually producing a second revolution, by making easy and fast most routine design tasks. However, the introduction ofComputer Aided OPTIMUM Designtechniques has not yet produced the expected third revolution, in spite of the big amount of research and the interest of its potential applications. The authors think that this fact is due mainly to the dispersion of the optimum design research, and to the lack of a well established doctrine.In this paper we approach the design process from a general methodological perspective, suitable to be applied to a wide range of problems. The design process is organized in several related levels. This approach leads naturally to the concept of optimum design and to the statement of a general mathematical programming problem. The practical application of this methodology to any particular problem takes an efficient and modular form. First and second order sensitivity analysis techniques are introduced from the general formulation, and alternative techniques (adjoint state) of the direct differentiation method are discussed.DAO2, a powerful and versatile computer aided optimum design system by the Finite Element Method, has been developed by the authors1according to this general methodology. The system can solve efficiently 2D and 3D structural fixed‐geometry and shape optimization problems. The power and viability of this methodology is illustrated by the solution to a structural optimization problem. The shape of the central section of an arch dam is optimized. A linear elastic structural FEM analysis is simultaneously performed for plane stress and for radial symmetry—while constraints are imposed for several load cases—taking into account the construction and loading stages. It should be emphasized that the same optimum design is reached in a small number of iterations starting from two significantly different