The main purpose of this research is to develop optimal cable arrangement and the damping of nonlinear structural system reinforced by non-compression resistant cables when it vibrates. The object is the moment-resisting frames which reinforced by the no initial tension cable. First, we clarified the cable arrangement which could lower the displacement at the time of the earthquake vibration by analysis using 3-layer 2-span moment-resisting frames which installed cables. Second, we conducted free vibration experiment using small models. It was revealed that there was damping peculiar to non-linear vibration to the structure reinforced cables from the result. It could be considered to be damping by a cable repeating the tension state and the deflection state.