In Japan, about seventeen nuclear power stations are operating. The energy generated by nuclear power stations is about 30 percent of gross generated electric power in Japan. A lot of spent fuels come out of the nuclear power stations. The spent fuels are stored in a canister which is put in a concrete cask until reprocessed in the reprocessing facility. The cask is generically free-standing on a horizontal floor. Recently, the huge earthquakes frequently arise, so it is necessary to prevent the cask from overturning and the canister from breaking when an earthquake occurs. In this study, the cask-canister system is considered as a dual structure. The structure is freely standing on the floor. We analyze sliding and rocking motions of the structure subjected to a horizontal earthquake excitation.