This paper describes design methods of passive vibration suppression in flexible structures using piezoelectric elements. The piezoelectric device on the structure with an inductance and a resistance connected in series or parallel works like a mechanical dynamic vibration absorber. However, until now the optimum value of the resistance had not been formulated for each series or parallel connection. In this study, new formulations were derived by making use of the two fixed points method, and their effectiveness was investigated by calculation and experiment. Furthermore, formulations to obtain the optimum values for mobility and accelerance were also derived.