Abstract: With the aid of the integral transformation, thesymplectic system is introduced into the problem of two-dimensionalthermo-viscoelasticity and the dual equations of the fundamental problem areconstructed. All solutions of Saint-Venant problems can be obtained directlyvia zero eigenvalue eigensolutions, which satisfy the conjugatedrelationships of the symplectic orthogonality. Meanwhile, an effectivemethod for boundary problems is provided by thetechnologies of variable substitution and eigensolution expansion. Numericalexamples show that the symplectic method is effective for sometypical boundary problems with creep andrelaxation characteristics of thermo-viscoelasticity.