Abstract: A higher order displacement mode is presented for sandwich shells including shear deformation in composite face layers.The mode satisfies the condition that the transverse shear stresses vanish on the sandwich shell top and bottom surfaces.From this mode the finite element equations are derived for free vibration of sandwich shells.The damping characteristics of the core and face layers are discussed.And the formula of damping matrix is given.The comparisons between numerical computed values and experimental data are carried on.Finally,the curves which the damping ratio Ψ varies with the core thickness h_c,shear modulus G and damping loss factor β,are shown graphically.