Disclosed herein are methods of electrospinning poly(glycerol sebacate) (PGS) which allow stable PGS fibers and fibrous PGS constructs, scaffolds and grafts to be formed. In one example, a disclosed method includes generating PGS fibers by blending PGS prepolymer with a heat resistant synthetic carrier polymer, wherein the blend is electrospun into micro- or nano-fibers, and the PGS prepolymer is cross-linked into PGS with heat without using chemical cross-linkers. In another example, a disclosed method includes electrospinning a PGS and gelatin blend, wherein the PGS and gelatin composition are cross-linked by heat curing without using chemical cross-linkers. In another example, the method includes preparing an electrospinning precursor solution comprising blending PGS prepolymer with poly(lactic-co-glycolic acid) (PLGA) and a chemical cross-linker; electrospinning the prepared blend; and exposing the electrospun blend to an organic solvent to remove the PLGA.