1 Abstract This work presents the Two-phase method for fuzzy optimization of cable stayed bridges. The minimization problem is stated as the minimization of stresses, displacements and bridge cost. A finite-element approach is used for structural analysis. It includes a direct analytic sensitivity analysis module, which provides the structural behaviour responses to changes in the design variables. An equivalent multicriteria approach is used to solve the non-differentiable, non-linear optimization problem, turning the original problem into the sequential minimization of unconstrained convex scalar functions, from which a Pareto optimum is obtained.In the first phase the fuzzy solution is obtained by using the Level Cuts Method and in the second phase the crisp solution, which maximizes the membership function of fuzzy decision-making, is found by using the Bound Search Method. Illustrative numerical examples are solved. Keywords: Fuzzy optimization, cable-stayed bridges, structures. 1 Introduction Cable-stayed bridges are large and expensive structures that are now being widely used. The trend to increase the spans and the advent of innovative erection techniques make thus desirable the development of computational tools to assist on the preliminary design stage and/or erection control, which today relies mostly on the design staff expertise. The authors have been involved in the last few years in such a project, which led to the development of a programme dealing with the aspects of design which can be objectively expressed by a numerical merit measure. The optimization can be stated as that of the minimization of structural cost or volume, and the maximum stresses throughout the structure. Additional objectives are aimed at the deflections or displacements and to guarantee that the design variables are at least specified minimum values. This work started with the shape Paper 100 Optimum Design of Cable-Stayed Bridges with Imprecise Data L.M.C. Simões and J.H. Negrão Department of Civil Engineering, University of Coimbra-Polo II, Coimbra, Portugal 2001, Civil-Comp Ltd., Stirling, Scotland Proceedings of the Eighth International Conference on Civil and Structural Engineering Computing, B.H.V. Topping (Editor), Civil-Comp Press, Stirling, Scotland.