Based on the basic equations of free vibration of thin plate, the Hamilton canonical equations were obtained. By variable selection of moment, equivalent shear force, rotation angel and deflection forming dual variables, the analytical solutions for free vibration of thin plate were obtained under different boundary conditions, which were divided into symmetrical and asymmetrical about xaxial. The computational example of a quadrilateral rectangular plate bending was given, which demonstrated the effectiveness of the proposed method, thus extending the application of Hamilton system.