Abstract: The present invention is a shoe sole comprising an array of elliptical cells, wherein each cell has a wall, and wherein each cell wall is conjoined to or contiguous with at least one other cell wall. The cell wall may be conjoined to another cell wall by a conjoining element. At least some of the cell walls buckle when compressive or shear force is applied during use. The sole is made from any material with elastic properties for this application. The shoe sole can further comprise a substrate, also made of elastomeric material, integrated with the cell walls at their upper level, lower level, or their periphery, forming a unitary piece. Variations can be made as to the dimensions and arrangement of these cell walls. This sole can be incorporated into a shoe sole assembly as a shoe midsole.