This paper discussed the chaotic phenomenon of equilibrium of a thin elastic rod with noncircular cross section under the action of torques on both ends. The equilibrium equations of the rod were written on the basis of Kirchhoff's kinetic analogy. The chaos was caused by the small periodic variation of the bending stiffness of the rod. The Melnikov's method was applied to predict the existence of the chaos, and the Poincaré sections, as well as the phase trajectory were given as numerical verification. It was shown that the rod had a chaotic configuration in the sense of Smale horseshoe. The geometric shapes of the rod with chaotic and regular behavior are presented.