This paper describes a new hybrid vibration suppression technique for flexible structures like beams and plates using piezoelectric elements and analog circuits. There are two main methods to suppress vibration of flexible structures. One is active vibration control and the other is passive vibration suppression. The former is often effective but has a stability problem. While the latter avoids such instability, its controlling force is small. Hence, this paper is proposing a new hybrid vibration suppression method that is stable and effective. The optimum values of the circuit are determined by simple formulations derived by Two Fixed Points Method. The proposed method is verified by experiments that demonstrate that the hybrid method works better than conventional passive vibration suppression methods.