Disclosed herein is a thin-walled cylindrical stent in which one or more of the sets of strut members are more radially rigid after stent expansion as compared to other sets of strut members. Each set of strut members consists of a multiplicity of structural struts that are connected together with the struts extending circumferentially when the stent is outwardly radially deployed within a vessel of a human body. The sets of strut members are those parts of the stent which unfold during radial expansion and provide the radially rigid structure which maintains vessel patency. This invention is a stent structure specifically designed to have enhanced radial rigidity either at the ends or the center of the stent. More radially rigid end struts reduce injury to the vessel from over expansion at the ends of the stent. The embodiment of the present invention with enhanced rigidity in the center would be particularly useful for the treatment of calcified obstructions. Enhanced rigidity can be achieved by either having a set of strut members that becomes more ring-like when radially deployed, or the strut members have a greater width as compared to other strut members of the stent.