In structural design, expensive function evaluations can be replaced by accurate function approximations to facilitate the effective solution of multiobjective problems. In this paper we address the question: How can we solve multiobjective shape optimization problems effectively using a Design-of-Experiments (DOE) -based approach? To answer this question we address issues of creating non-orthogonal experimental designs, when dependencies among the parameters that represent shape functions are present. A screening strategy is used to gain knowledge about the structural behavior within the design space and the trade-off among multiple design objectives is efficiently modeled through employing response surfaces during design optimization. The shape optimization of a flywheel where two conflicting design goals are present is used to illustrate the approach. Our focus is on the method rather than the results per se.