A stent incorporating flexible, preferably polymeric, connecting elements into the stent wherein these elements connect adjacent, spaced-apart stent elements. Preferably the spaced-apart adjacent stent elements are the result of forming the stent from a helically wound serpentine wire having space provided between adjacent windings. Other stent forms such as multiple, individual spaced-apart ring-shaped or interconnected stent elements may also be used. The connecting elements are typically web-shaped and result from creating slits or apertures in a covering of graft material applied to the stent and then, for example, applying heat to cause the slits or apertures to enlarge. The remaining graft material forms the interconnecting webs between the adjacent stent elements.