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In the present paper, finding the exact bound of structural response for truss structures is considered under bounded interval type uncertainty. This problem is challenging since seeking the exact bound corresponds to locating the global optima of a multivariate function (generally nonconvex). Traditional treatment of this problem involves the solution of a linear mixed 0-1 programming problem, which is a highly computationally demanding task especially when large-scale structures are taken into consideration. In order to alleviate the computational effort, a sensitivity bounding technique is developed in this work using the tools from convex analysis to disclose the monotonicity of concerned structural response function with respect to 0-1 variables. It is shown that this technique can not only reduce the number of 0-1 variables substantially but also change the computational complexity of the considered problem from nondeterministic polynomial-hard to nondeterministic polynomial-hard in some cases. The proposed approach provides the possibility of finding the exact bound of structural response for large-scale truss structures within a reasonable time, and its effectiveness is demonstrated through several numerical examples. KEYWORDS bounds of structural response, global optimization, interval uncertainty, linear mixed 0-1 programming, sensitivity bounding Int J Numer Methods Eng. 2018;116:21-42. wileyonlinelibrary.com/journal/nmewhere x, f (x), and g i (x; p) are the design variable vector, objective function, and ith constraint, respectively. p denotes the vector of uncertain parameters and U p is the corresponding uncertainty set. It is clear that the objective of a WCDO problem is essentially to optimize the performance of a design while ensuring the its safety under the worst combination of uncertain parameters. Therefore, Equation (1) is actually a nested bilevel program. The upper level program aims at finding the best design by selection of optimal design variables, while the lower level program identifies the worst-case structural responses and determines the feasibility of a given design. To predict the extreme structural response with respect to the uncertain parameter efficiently, interval analysis technique or convex modeling methods cooperating with sensitivity analysis and gradient-based algorithms are commonly adopted in literatures. [8][9][10][11][12] It should be pointed out that the lower level program in Equation (1) must be solved with global optimality; otherwise, the feasibility of an "optimal solution" cannot be fully guaranteed. 13 This issue, however, cannot been guaranteed by the general gradient-based algorithms used in most related literature studies, especially for WCDO problems involving nonconvex objective/constraint functions, which are ubiquitous in practical engineering applications. Under this circumstance, the obtained solution may be totally meaningless since the worst-case structural response may be severely underestimated. Actually, it is very difficult to find the global ...