Abstract: Constitutive relations of laminated composite plates and classic Kirchhoff plate theory are used to deal with the relationship between stress-strain and transverse deflection of unidirectional composites with interleaved viscoelastic damping layers.The interleaved viscoelastic layers are treated as isotropic materials.The transverse shear strains are obtained according to equilibrium equations.Their boundary conditions and continuity conditions are satisfied.Strain energy stored in in-plane as well as in transverse shear is considered.The Ritz method is employed to research the strain energy of individual stress components.The fundamental theory is introduced and the in-plane strain energy is discussed.