Abstract: A vascular graft in the form of a tube or flat sheet of biocompatible material having an outer covering of deflectably secured material such as porous film, fibers, discrete pieces of material, or combinations thereof. Two different types of fibers may also be used. The vascular graft may be of tubular form for replacing or bypassing entire segments of veins or arteries or alternatively may be in the form of a flat sheet useful for repairing portions of the circumference of veins or arteries. The tube or flat sheet of biocompatible material and the outer covering of deflectably secured material are preferably of porous polytetrafluoroethylene. The inventive vascular graft is useful for dialysis access in that it offers a reduction in blood leakage when the vascular graft is punctured by a dialysis needle and the needle is subsequently removed. It is also useful for reducing suture hole bleeding resulting from holes created through the graft by penetration of the graft with a suture needle.