A sole structure of an article of footwear has a support assembly structure including a flexure element and an upper support element. The flexure element may have a central portion located between first and second ground-contacting or lower regions, wherein the central portion may have a downwardly concavely-curved shell-like region. The flexure element also may have first and second flanges extending upward from the first and second lower regions, respectively. The upper support element is positioned above the central portion and between the first and second flanges of the flexure element. When a vertical compressive load is first applied to the upper support element, the upper support element moves vertically relative to the first and second flanges. An article of footwear having the sole structure attached to an upper is also provided.