Abstract: In this paper the solutions of von Kármán for elastic large deflection problem are classified as the several solutions of Schrödinger equation for quantum eigenvalues problem, and we present the transform for elastic large deflection problem from non-linear equation into linear equation. Thus, we create favourable conditions of the adoption of converse scattering methnd and Bácklund transformation. We also discuss the large deflection problem of long and narrow plate.We can study the non-linear transition of elastic thin plate by furnished method from this paper.