Hamiltonian system used in dynamics is introduced to formulate the transversely isotropic magnetoelectroelastic solids plane problem in rectangular domain and symplectic dual equation is derived corresponding to the generalized variational principle of the magnetoelectroelastic solids. The equation is expressed with displacements, electric potential and magnetic potential, as well as their duality variables--lengthways stress, electric displacement and magnetic induction in the symplectic geometry space. Since the x-coordinate is treated as time variable so that z becomes the independent coordinate in the Hamiltonian matrix operator. The symplectic dual approach enables the separation of variables to work and all the Saint Venant solutions in the symmetric deformation are obtained directly via the zero eigenvalue solutions and all their Jordan normal form of the corresponding Hamiltonian operator matrix and the boundary condition. An example is presented to illustrate the proposed approach.