Finite element analysis of sandwich and laminated composite structures with viscoelastic layers is performed. The present implementation gives the possibility to preserve the frequency dependence for the storage and loss moduli of viscoelastic materials exactly. Moreover, the storage and loss moduli in this case are defined directly in the frequency domain by an experimental technique for each material and can be used after curve fitting procedure in the numerical analysis. Damping characteristics of viscoelastic composite structures are evaluated by the energy method, the method of complex eigenvalues, from the resonant peaks of the frequency response function and using the steady state vibrations. Numerical examples are given to demonstrate the validity and application of the approaches developed for the free vibration, frequency and transient response analyses.