This paper presents semidefinite programming approaches for computing confidential bounds for the dynamic steady-state responses of a damped structure subjected to uncertain driving loads. We assume that amplitudes of harmonic driving loads obey a non-probabilistic uncertainty model. The semidefinite programming problems are formulated for finding confidential bounds for various characteristic amounts of dynamic steady-state response, including the modulus and phase angle of the complex amplitude of the displacement and stress. Numerical examples demonstrate that sufficiently tight bounds can be obtained by solving the presented semidefinite programming problems. (C) 2009 Elsevier B.V. All rights reserved.