A two-chain insulin analogue contains a modified A-chain polypeptide and a modified B-chain polypeptide. The A-chain polypeptide comprises one or more of: a His or Glu substitution at position A8, a Glu substitution at position A14； and a Gln or Arg substitution at positon A17. The B-chain polypeptide comprises one or more of: a deletion of the amino acids at position B1, B1-B2, B1-B3, B30 or a combination thereof； an Ala or Glu substitution at position B2； a Glu substitution at position B3. The analogue exhibits thermodynamic stability in a zinc-free solution, decreased self-association, maintains biological potency, and no increased mitogenicity. The analogue exhibits resistance to chemical degradation and physical degradation. A method of treating a patient with diabetes mellitus or obesity comprises administering a physiologically effective amount of the insulin analogue or a physiologically acceptable salt thereof to a patient.
