The supercoiling configuration of a thin elastic rod is discussed on the basis of Kirchhoff’s model. The equivalent twisting stiffness and bending stiffness of a thin helical rod are derived. The stability and bifurcation of a thin elastic rod under tension and twist are analyzed, and the results can be applied to determine the stability of a thin helical rod by use of the equivalent stiffness. In the case when the rod is under constant twist and increasing tension force the straight equilibrium can be unstable and transfers to helical equilibrium. When the tension force increases further the straight thin helical rod can be unstable and twins to a supercoiling state. Therefore the forming process of supercoiling configuration of a rod under tension and twist observed in Thompson/Champney experiment can be explained qualitatively.