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An investigation has been performed to study the response of the front bumper beam of automobiles subjected to an external impact load. In the investigation, an aluminum shell structure is modeled as a beam, and the energy absorber of polyurethane is also modeled as statically equivalent springs attached to the beam. Castigliano's second theorem and principles of energy and momentum are then used to calculate the reaction forces and maximum deflection. Stress distribution is then calculated using the beam theory. The primary concern of the investigation is to present a procedure of how to design optimally the cross-sectional shape of the front bumper of automobiles.