The problem on stability of equilibrium of a thin elastic rod in view of dynamics is discussed in this paper. The dynamical equations of the rod is established, and the definitions of Lyapunov stability for a discrete dynamical system with arc-coordinate s and time t as double arguments are proposed. As an example, the stability of straight equilibrium of a rod with noncircular cross-section and intrinsic twisting is analyzed by use of the first approximation method. It was proved that the straight equilibrium of the rod is stable dynamically when the conditions of stability are satisfied within the scope of statics.