Abstract: This paper discusses the setting and numerical solution ofthe non-probabilistic reliability-based structural optimization problem.Based on the convex model description for parameter scatters, the optimaldesign of non-deterministic structures is formulated as a nestedoptimization problem, in which the inner loop concerns a Min-max problem forevaluation of the reliability index. A performance measure-based method isproposed, where the feasibility of a design is determined throughminimization of the performance function value within the parameter domain.The expensive computation of the non-probabilistic reliability index, asneeded in the conventional approach, is thus avoided. The proposed approachis applicable to structural optimization problems accounting for deviationsof material properties, geometrical dimensions and loading conditions.Moreover, the design sensitivity of the minimum performance function valuecan be readily evaluated. Numerical examples show the validity andefficiency of the present method.