Abstract: The paper describes the strategies for constraint function robustness and objective function robustness respectively subject to probabilistic and non-probabilistic uncertainties and proposes an approach to robust design of structures with probabilistic and non-probabilistic uncertainties. The robustness of constraint functions is achieved by adding some items reflecting the variation of the constraint function due to uncertain variables to the original constraint function. The robustness of objective function is guaranteed by adding several new objective functions about the sensitivities of the original objective function and performing a multi-objective optimization. The proposed method is applied to the design of a 10-bar truss structure and the modified lexicographic method is employed to find the optimal solution. Numerical results show that the degree of objective function robustness decreases as the uncertainty degree of variables increases for the same structural weight while the degree of objective function robustness increases as the structural weight increases for the same uncertainty degree of variables.