In this paper the feasibility of using a particular feasible direction interior point algorithm for solving reliability- based optimization problems of high dimensional stochastic dynamical systems is investigated. The optimal design problem is formulated in terms of an inequality constrained non-linear optimization problem. A class of interior point algorithms based on the solution of the first-order optimality conditions is considered here. For this purpose, a quasi-Newton iteration is used to solve the corresponding nonlinear system of equations. Several numerical examples are presented to illustrate the feasibility of the proposed methodology.