Firstly, based on the appropriate definition of symplectic inner product, the forced vibration problem of orthotropic rectangular thin plate was introduced into symplectic duality system, so an analytical approach for the steady state solution of forced vibration was presented by employing variables separation and eigenfunction expansion. Secondly, the symplectic eigenproblems for the forced vibration of the orthotropic rectangular thin plates with two typical boundary conditions, i.e. opposite sides simply supported and opposite sides clamped, were discussed. And the transcendental equations of symplectic eigenvalues and the symplectic eigenvectors were given in analytical form. Lastly, analytical solutions of two examples were presented by using this method. And the solution of a fully simply supported plate under uniformly distributed harmonic load was chosen to compare with the classical Navier’s method, and the result shows that the new technique not only has good accuracy but also has better convergence speed than the classical methods, especially on internal forces.