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Sandwich panels with crushable foam cores have attracted significant interest for impulsive load mitigation. We describe a method for making a lightweight, energy absorbing, glass fiber composite sandwich structure and explore it is through thickness (out-of-plane) compressive response. The sandwich structure utilized corrugated composite cores constructed from delamination resistant 3D woven E-glass fiber textiles folded over triangular cross section prismatic closed cell, PVC foam inserts. The corrugated structure was stitched to 3D woven S2-glass fiber face sheets and infiltrated with a rubber toughened, impact resistant epoxy. The quasi-static compressive stress-strain response of the panels was experimentally investigated as a function of the strut width to length ratio and compared to micromechanical predictions. Slender struts failed by elastic (Euler) buckling which transitioned to plastic microbuckling as the strut aspect ratio increased. Good agreement was observed between experimental results and micromechanical predictions over the wide range of core densities investigated in the study.