a pattern of fine perforations in the form of substantially one dimensional slits 14 extending across the cover 39 s entire surface in this particular embodiment the slits are distributed in a substantially uniform pattern across the entire surface area of the stent cover it is to be additionally noted that the slits are each arranged in a substantially longitudinal orientation the use of the cover is not limited to any particular type of stent nor to any particular method of deployment nor for any particular application the stent cover is stretched tightly over stent 15 and is intended to cover some or all of the stent it may be desirable to have the cover overlay only a portion of the stent so that the exposed stent portions can embed in the vessel wall to more firmly implant the stent the stent cover shown in fig1 is shown in an expanded condition in fig2 each of the slits has assumed a generally oval configuration 14 a as is the natural result of stretching a material initially having a straight perforation of constant width formed therein as shown in fig3 an alternative embodiment stent cover 16 utilizes a varying pattern of slits 18 each slit is of the same length but the density of slits varies along the length of the stent in this particular embodiment the density of slits is much lower in the regions 20 near the ends of the stent than in its central region 22 as a result upon expansion the cover will offer greater resistance to radial expansion near the ends than in the central region of the stent.