The purpose of this study is to reveal the dynamic mechanism, which governs the complicated vibration phenomena of an elasto-plastic system with geometrical nonlinearity, from the viewpoint of the theory of nonlinear vibration. The periodic solution and its stability are discussed for an Blast o-plastic single-degree-of-freedom system. The influence of the geometrical nonlinearity on the elasto-plastic vibration and the instability caused by the plasticity are explained with these periodic solutions. The comparison between the periodic solutions and the time-domain responses on the phase plane shows several interesting characteristics suggesting the mutual relation.