A self-sealing vascular graft with kink resistance is described. The vasculargraft includes a substrate that can be a PTFE, having a self-sealing regionthat may include several layers of material. The central section of thevascular graft may be constructed differently from surrounding self-sealingregions, in order to provide kink resistance following the clamping of thegraft. Also described is a graft with a flared cuff attached to one or bothends, the attachment or transition region including reinforcement beading.