Soil-structure interaction (SSI) system is composed of soil and structure that are two materials with quite different damping behaviors and it is regarded as non-classical damping system in conventional concept. Based on the analysis of motion state of SSI system, the paper presents the damping characteristic of SSI system via shaking table test. The results of transfer function, acceleration response time histories and equivalent viscous damping ratio and so on indicate that under certain conditions, SSI system shows approximate classical damping characteristic. In practical projects, dynamical analysis of SSI system can be viewed as approximately classical damping system once the synergistic effect of soil is considered. •The damping characteristics of soil-structure interaction (SSI) system were investigated.•Identification method of SSI damping system was firstly developed.•A collaborative mechanism between soil and structure was observed after small excitation.•The interface of energy transfer soil-structure interaction system was observed to be integral.•SSI system can be viewed as approximately classical damping system.