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The helical equilibrium of a thin elastic rod has a practical background such as DNA, fiber, sub-ocean cable and oil-well dill string.The stability problem of helical equilibrium of an elastic rod has been studied on the basis of Kirchhoffs model.The main hypotheses of Kirchhoffs theory including no extension of the centerline and no shear deformation of the cross section are not adaptable to the real soft materials of biological fibers.The exact Cosserats model incorporating the tension and shear deformation is a better presentation of the real dynamic process of a rod in practice.