The present invention provides for an expandable stent (10 or 20) for use in an artery or other vessel of a human body. The stent structure (10 or 20) maintains the patency of the vessel within which the stent (10 or 20) is expanded radially outward. One embodiment of the present invention is a stent (10) having a multiplicity of frames (12) joined together by at least two undulating longitudinal structures (14L and 14R) which can readily change their length in the longitudinal direction so as to provide increased longitudinal flexibility for the stent (10) for easy passage through and placement within a curved vessel such as a coronary artery. The stent (20) is an embodiment of the present invention having frames (22) joined with longitudinal structures (24B, 24T and 24R) and formed from a single, thin-walled piece of metal by means of laser cutting or chemical etching. Because the stent (20) is fabricated from a single piece of metal, it provides a multiplicity of closed perimeter cells that are formed as a continuous metal structure.