An article of footwear is disclosed that includes an upper and a sole structure secured to the upper. The sole structure includes a midsole element, an upper sheet, and a lower sheet. The midsole element has an upper surface and an opposite lower surface. In addition, the midsole element defines a plurality of bores extending from the upper surface to the lower surface. The upper sheet is secured to the upper surface and extends over at least a portion of the bores. The lower sheet is secured to the lower surface, and the lower sheet is positioned to correspond in location with the upper sheet and extend under the portion of the bores.