Small-diameter vascular grafts perform poorly as arterial bypasses. We developed a cell-free, resorbable graft intended to remodel in situ into a living vessel. The graft consisted of a soft electrospun poly(glycerol sebacate) (PGS) core, a PGS prepolymer (pPGS) coating, and a reinforcing electrospun poly(ε-caprolactone) (PCL) sheath. The core contained 4.37 ± 1.95 μm fibers and had a porosity of 66.4 ± 3.2%, giving it large pores to encourage cellular infiltration and pro-healing macrophages. The sheath contained 6.63 ± 0.89 μm fibers and had a porosity of 80.5 ± 2.1%. in vitro testing suggested that the stress achieved at arterial pressure would be 13-fold lower than the yield stress of the graft. Grafts were implanted as 7 cm carotid interpositions in two sheep. Sheep were maintained on dual antiplatelet therapy and followed with duplex ultrasound. One graft ruptured at 13 days. The second animal was euthanized with a dilated graft at 15 days. Histology showed near-total degradation of the core and a robust inflammatory response within the sheath. Little neotissue had formed within the graft wall or lumen, but the graft had become surrounded by fibroblastrich and vascularized connective tissue. Because PCL is commonly used in resorbable grafts, this mechanical destabilization was unexpected. We speculate that the inflammatory response instigated by the rapidly degrading PGS intensified degradation of the PCL and that the large pores enabled a prolonged acute host-graft reaction which attacked the entire bulk of the material, speeding weakening. Future work will focus on how to moderate inflammation and improve remodeling of grafts in large animals.