Bumpers are structural components to reduce physical damage to the front and rear ends of a passenger motor vehicle from low speed collisions. Damage assessment and the protectiveness are the commonly used designing criteria but in this study, relative displacements of the bumper are examined. To absorb the crash energy without significant damage to the bumper itself, foam material is installed between fascia and beam. However, it is not easy to predict the exact displacements generated in bumper structures through FEM because the compressive stress-strain curve of a foam material depends on strain rates that deviates significantly on each trial. Under this uncertain condition, a range of displacements is calculated and the optimum design is performed using the design of experiments. The result will be used to find the design that minimizes the weight within displacement constraints. The orthogonal array of L9 is introduced to find the optimum of the design variables that considers the thickness of inner beam, outer beam and stay, This study will suggest the design procedure of a front bumper using the uncertain stress-strain curve of a foam material.