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The decay of shocks in laminated composites is investigated with numerical modeling. An anomalous effect of the cell size on the leading shock amplitude was found. It is manifested in increased amplitude of the leading shock wave with the increase of the number of interfaces between the materials with different acoustic impedances crossed by a “long” shock wave in periodic laminar composites. The components in the fine composite are loaded by a larger number of shock waves than in the coarse composite, resulting in a higher residual temperature in the fine composite. The anomalous attenuation is not observed for “short” waves at the same depth from the impacted surface. The bonding strength between the layers has only a slight effect on the shock evolution. © 2001 American Institute of Physics.