In this paper, the mitigation of the seismic response of connected cabinets and the electronics inside them when using elasto-plastic dampers installed between cabinets is reported. In many plants, such as power and chemical plants, several rectangular cabinets, which contain electronics, are set directly on the floor in the buildings. The electronics inside the cabinets are extremely important for controlling the behavior of the plant. When an earthquake occurs, the cabinets and inside electronics overturned by a rocking motion and may be damaged or destroyed. Even if the cabinets are not overturned, there is a concern that large accelerations will be applied to the internal electronics owing to the seismic wave. As a result, the full plant cannot be controlled, and a serious accident may occur. Therefore, it is necessary to develop methods that can simultaneously reduce rocking motion and prevent internal electronic damage. In some cases, the cabinets cannot be connected to the wall or floor for a particular reason. Even in this case, connecting the adjacent cabinets with an elasto-plastic damper, which is a nonlinear damper, can mitigate the vibrations of the cabinets and electronics. We consider the behavior of adjacent cabinets with electronics connected using two elasto-plastic dampers. The cabinets are modelled by the rigid bodies rotating around their corners, and the internal electronics are modeled as rigid bodies moving in the translational direction in the cabinets. The elasto-plastic damper has bilinear hysteretic characteristics and can absorb the energy of the earthquake inputs. The rocking behaviors of the cabinets and accelerations of the electronics are investigated when the seismic wave is input to the connecting cabinets storing the electronics. The effects of the elasto-plastic damper on the mitigation of the rocking motions of the cabinets and the accelerations of the electronics were investigated. In particular, the attachment positions of the elasto-plastic dampers are important parameters for reducing the vibrations of the cabinets and electronics. Finally, the effects of the attachment position of the elasto-plastic damper are discussed.