A numerical method based on the semidefinite program is proposed 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. 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.