Abstract:Ultra-slender elastic rods are important models for describing the supercoiled configuration of DNA molecules, the growth configuration of biological systems, etc. Due to the existence of factors such as the super-large deformation, complex contact and growth of DNA molecules, it brings difficulties to their modeling and calculation. The analytical mechanics method of ultra-slender elastic rods established based on the Kirchhoff dynamics analogy has opened up a new way for their modeling and analysis. This paper reviews the analytical mechanics methods of slender elastic rods and their extensions and applications in growing elastic rods and stability, and looks forward to future developments.