Prosthetic vascular grafts frequently occlude in small-diameter (< 6 mm) applications. Resorbable synthetic grafts might offer an economical way to produce living vessels for transplant instead. After implantation, these grafts are degraded by infiltrating host cells, which then build up a new, artery-like conduit in place of the foreign material. Previous work in the rat aorta demonstrated that resorbable grafts based on the fast-degrading elastomer poly(glycerol sebacate) (PGS) produced high-quality neoarteries with strong patency and native-like architecture. But those PGS-based grafts could not be produced at human sizes. In this dissertation, PGS-based grafts were developed using electrospinning, which is a more scalable and adaptable production method. The first graft prototype was tested in the mouse aorta. Grafts showed strong patency and mechanical stability, but the small pores in the electrospun PGS prevented timely degradation and neotissue formation. Therefore, a second prototype with larger pores was implanted in pigs as arteriovenous shunts. These grafts showed improved cell infiltration and early signs of remodeling. But the reinforcing composite sheath layer was kink-prone, and grafts eventually collapsed and thrombosed under compression from animal motion. Finally, a third prototype with large pores and improved kink resistance was implanted in the sheep carotid. These grafts showed extensive cellular infiltration and rapid degradation, leading to dilation and rupture. Though a successful prototype has not yet been achieved, we have now established a versatile and scalable fabrication process that can generate scaffolds with a range of degradation rates, from too slowly-degrading (mouse) to too quickly-degrading (sheep). Adjustments to scaffold design should locate the degradation rate matching the rate of neotissue formation somewhere in the middle.