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The paper concentrates on the study of propagation of thermoelastic waves in a homogeneous, transversely isotropic, thermally conducting elastic plate bordered with layers (or half-spaces) of viscous liquid on both sides in the
context of non classical theories of thermoelasticity. Complex secular equations for symmetric and antisymmetric wave motion of the circular plate, in completely separate terms, are derived. Finally, in order to illustrate the analytical results, the numerical solution is carried out for transversely isotropic plate of cobalt material bordered with water by using the functional iteration method.