Abstract: The perturbation-based stochastic finite element analysis incorporating structuraloptimization techniques is employed in the structural robust design problem. In the framework ofthe second-order perturbation-based stochastic finite element method, the computational schemesfor the expected value and the variance of the structural performance functional as well as theirsensitivity are proposed. The robust design of structures is formulated as a multi-criteriaoptimization problem, in which both the expected value and the standard deviation of theobjective function are to be minimized. The robustness of the design feasibility is also accountedfor by involving the variability of the structural response in the constraints. The optimizationproblem is converted into a scalar one and solved by a gradient based optimization algorithm. Todemonstrate the applicability of the presented method, numerical examples are given.