Composite structures with elastic layers and viscoelastic core have been used as a passive damping treatment applied to reduce vibration amplitudes. In the design phase of this type of damping technique, many aspects ranging from computer modeling to laboratory tests should be considered. Due to the frequency dependency of mechanical properties of these materials, time domain based models for viscoelastic materials are not as numerous as frequency domain based methods. Usually, time domain methods introduce extra dissipation coordinates or internal variables as Golla-Hughes-McTavish (GHM) method and also Anelastic Displacement Field (ADF) method. In this paper, these methods are evaluated by comparing theirs results to the ones obtained by means of theoretical analysis. Processing time are also evaluated highlighting advantages and disadvantages of these methodologies. Finally, these two time domain methods are applied to a real structure, pointing out the facilities and difficulties to simulate an actual situation.