Embodiments relate to amino acid-based poly(ester urea)s with amino acid residues selected L-leucine, L-isoleucine, L-valine or combinations thereof. The amino acid-based poly(ester urea)S may optionally include a second amino acid residue selected from proteinogenic amino acids and non-proteinogenic amino acids. The amino acid-based poly(ester urea)s are particular useful for the preparation of vascular grafts. Due to the biocompatibility of the amino acid-based poly(ester urea)s, vascular grafts prepared from amino acid-based poly(ester urea)s with small internal diameters (i.e. less than 5 mm) may be prepared and inserted into a patient or animal, and provide a substantial decrease in the risk of failure compared to conventional polymers used in vascular grafts.