This contribution focuses on reliability-based design and optimum design sensitivity of linear dynamical structural systems subject to Gaussian excitation. Directional Importance Sampling (DIS) is implemented for reliability assessment, which allows to obtain first-order derivatives of the failure probabilities as a byproduct of the sampling process. Thus, gradient-based solution schemes can be adopted by virtue of this feature. In particular, a class of feasible-direction interior point algorithms are implemented to obtain optimum designs, while a direction-finding approach is considered to obtain optimum design sensitivity measures as a post-processing step of the optimization results. To show the usefulness of the approach, an example involving a building structure is studied. Overall, the reliability sensitivity analysis framework enabled by DIS provides a potentially useful tool to address a practical class of design optimization problems.