Stent designs for use in vessels, such as the carotid and coronary 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 form a generally serpentine wave pattern transverse to the longitudinal axis between alternating valley portions and peak 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 inverted double-curved portions to connect the cylindrical element to the other adjacent cylindrical element. The stent designs include both a six crown and an eight crown stent which exhibit flexibility and sufficient radial strength to support the vessel.