The solution of reliability-based design optimization problems by using reduced-order models is considered in this chapter. Specifically, problems involving high-dimensional stochastic dynamical systems are analyzed. The design process is formulated in terms of a constrained nonlinear optimization problem, which is solved by a class of interior point algorithms based on feasible directions. Search directions are estimated in an efficient manner as a by-product of reliability analyses. The design process generates a sequence of steadily-improved feasible designs. Three numerical examples are presented to evaluate the performance of the interior point algorithm and the effectiveness of reduced-order models in the context of complex reliability-based optimization problems. High speedup values can be obtained for the design process without changing the accuracy of the final designs.