Abstract: By the Hamilton's principle, this paper presents a generalized formulation for modeling the system with passive piezoelectric shunt circuit. It is applicable to various structures and shunt circuits. Formulations of single-degree-of-freedom system for four types of piezoelectric shunt circuits, R-shunt –circuit, L-shunt –circuit, RL-series-shunt –circuit and RL-parallel-shunt –circuit, are obtained. The frequency response characteristics of the systems with these four passive piezoelectric shunt circuits are analyzed by numerical methods, and the effect of electrical and mechanical parameters on the system response is also investigated. Several conclusions and some problems to be studied in the future are highlighted.