A sealing structure for sealing a gap between a vacuum container 2 and a lid 3 contacted to an opening of the vacuum container 2 to close it. A cavity 66 is formed in an elastomer O-ring 64 interposed between the vacuum container 2 and the lid 3, and a cooling pipe 65 is inserted in the cavity 66. The O-ring is cooled by circulating coolant in the cooling pipe 65. Since permeability of gas in a solid depends on a temperature, the amount of gas permeating the O-ring 64, especially oxygen, can be reduced by cooling the O-ring 64, thus maintaining a vacuum level in the vacuum container 2 at a high level. Since the O-ring 64 is cooled from its inside, only the O-ring 64 can be cooled locally without influencing temperature controls at other parts of the vacuum device.