Passive damping augmentation is one of attractive methods for vibration suppression to various kinds of structures because it is definitely stable and generally simple. The system using thin film with viscous adhesive indicated a remarkable effect to the vibration suppression in the practical application to a satellite. To investigate its damping characteristic, several kinds of experiments have been performed. The results show that the non-linear behavior cause of non-Newtonian flow between shear load and shear deformation velocity in the viscous lamina of the thin film contributes to the damping capability. A mathematical model which consists of spring elements as film and friction elements as viscous lamina has been proposed from experiments. The simulational results with this present model are in good agreement with experimental ones.