Lyapunov stability of an elastic rod with non circular cross section in straight equilibrium was studied based on the thought of Kirchhoff kinetic analogy in the paper.Expressing the attitude of a section of the rod by Cardano angles,the equilibrium differential equation was established in terms of Kirchhoff theory of the rod, and its special solution when two ends of the rod were acted by a pair of force screws was found which stands for straight equilibrium state.The linear perturbation equation with periodic coefficient was obtained,where the period is directly proportional to the torque of the end and the length of the rod,and inversely as the torsion rigidity of the rod.The circular cross section of the rod was its special case.Lyapunov stability of equilibrium in the straight state was discussed according to the Floquet theory.It is explained that the torque and compressive force were advantageous to the stability and the tensile force wasn't by numerical examples.