The Schrödinger analogy of thin elatic rod is studied. Compared with the Kirchhoff dynamics analogy, the Schrödinger analogy is proposed. By the new analogy, the Kirchhoff equation of elastic rod can be written as curvature equation which is similar to nonlinear Schrödinger equation. Thus, the Jacobi elliptic function solution of Schrödinger equation can be taken into elastic rod equation. The space configurations of the elastic rod described by the solution are given. Schrödinger analogy reveals the relations between the quantum state of wave function and the geometry configuration of elastic rod, and gives a new way to solve the Kirchhoff equation.