An approach to study the sensitivity of dynamic responses for structural systems with respect to a set of design parameters is presented. The sensitivity is evaluated by considering the behavior of the system response when the design parameters vary within a given region of the design space. The sensitivity is computed by means of approximate responses, which are evaluated using approximation concepts. The approximation is based on modal analysis, and it is valid for general underdamped linear systems. Intermediate design variable and intermediate response quantity concepts are used to enhance the accuracy of the approximation. In this approach, modal energies and mode shapes are chosen as intermediate response quantities, and they are approximated in terms of selected intermediate system parameters. The approximation of these quantities requires a standard eigenvalue and eigenvector sensitivity analysis. Numerical results that illustrate the usefulness and effectiveness of the method are presented. Great insight into the behavior of the system can be gained using this methodology.