By applying the symplectic theory, the polarized axis of the piezoelectric medium is simulated as the time axis of the
Hamilton system, and the generalized displacement and stress, including electric induction and electric field, is
introduced, which can form the coupling variable. After these steps, complex energy density function about the
piezoelectric medium is introduced on the base of energy function, and then the coupling equations of the 3D
piezoelectric medium are founded according to the Hamilton variation principle. Separating variables in these coupling
equations, the basic equation of dynamics in the piezoelectric medium is derived under the Hamilton system. This
investigation can provide a new method, symplectic method, for the dynamic analysis of the piezoelectric medium.