Abstract: Analysis of the dynamic behavior of viscoelastically damped structures is studied. According to the constitutive relations of viscoelastic material expressed in fractional derivative operators, the analytical expressions of the mechanic properties of viscoelastic material are constructed by fitting the experimental data. A finite element model of sandwich beam with eight degrees of freedom is set up. Thereby, the finite element formulation of the motion equations is given for viscoelastically damped structure. A method for solving nonlinear eigenvalue problem by iteration is suggested to analyze the dynamic behavior of viscoelastically damped structure. The method has been applied to the complex model analysis of a sandwich cantilever beam with viscoelastic damping material core and verified experimentally. The agreement between the analysis and measurement shows that the method is reliable and practical and gives good accuracy.