Abstract: In this study, the characteristics of energy dissipation and vibration mitigation effect of classical inerter systems are studied through the energy analysis method. The series-parallel I inerter system (SPIS-I) is taken as an example to illustrate the method. The stochastic response formula for the single-degree-of-freedom structure with SPIS-I is derived under white noise excitation. The energy dissipation coefficient of the inerter system is defined to measure its energy dissipation and vibration mitigation effects. Using the response mitigation ratio-based design method, classical inerter systems are designed under the same target response mitigation ratio. Parametric analysis is conducted using the energy analysis method. The results obtained by the parametric analysis are verified by classical examples. The research results show that different inerter systems designed under the same target response mitigation ratio can effectively dissipate the structural energy. In the condition of the large target response mitigation ratio, the energy dissipation efficiencies of different inerter systems are similar, which are slightly influenced by the mechanical layout of the inerter system. When the response mitigation ratio is small, it is recommended to use an inerter system of series-parallel layout for more effective energy dissipation.