A mathematical model for the forced vibration of sandwich structures with a viscoelastic and piezoelectric layers is presented. The active-passive damping is realized by adding piezoelectric sensor and actuator layers to a sandwich viscoelastic structure. The mathematical formulation is developed in a general form in order to take into account for various viscoelastic models in the frequency domain. Frequency dependent Young modulus based on various Maxwell's model is used for viscoelastic materials modelling. A numerical method combining the finite element and perturbation methods called asymptotic numerical method is developed for the displacement and frequency dependent problem. Resonance curves for sandwich structures are obtained for various frequency ranges, excitation amplitudes and viscoelastic models. Only some matrix inversions and a few iterations are needed for large frequency ranges.