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To design a cost, weight, and energy efficient bumper foam energy absorber, it is important to consider optimizing the shape of coring employed in the design of the system. In this paper, a number of foam coring patterns are studied by both empirical and analytical methods. The size and shape of proposed core designs are studied in detail with consideration given to several different densities of expanded polypropylene (EPP) foam. Using the finite element method of structural analysis, it is possible to have an inside look at the stress distribution during deformation of foam structures. An optimization study using the finite element method is conducted using the energy absorption ratio as an efficiency parameter. Several coring patterns are studied and recommended for bumper foam core design based on high energy absorption efficiency and low tear stress.