Stent designs for use in peripheral vessels, such as the carotid arteries, are disclosed. The stents consist of a plurality of radially expandable cylindrical elements generally aligned on a common longitudinal stent axis and interconnected by one or more interconnecting members placed so that the stent is flexible in a longitudinal direction. The cylindrical elements are generally serpentine wave pattern transverse to the longitudinal axis between alternating valley portion and peak portions, the valley portion including alternating double-curved portions and U-shaped portions. The interconnecting members are attached to the double-curved portions to connect a cylindrical element to an adjacent cylindrical element and interconnecting members are attached to the U-shaped portions to connect the cylindrical element to the other adjacent cylindrical element. The designs include an eight crown and six crown stent which exhibit flexibility and sufficient radial strength to support the vessel.