Passive damping augmentation is one of attractive methods for vibration suppression to various kinds of structures because it is definitely stable and generally simple. Using viscous adhesive indicated a remarkable effect to the vibration suppression in the practical application to a satellite. In this paper, mathematical model of thin viscous adhesive layer using non-linear elements has been proposed. In this model, the characteristics of elements are correlated with non-linear internal phenomena of polymer. The simulation results using this proposal model are good agreement with experimental ones.