A vacuum vessel is provided in which the majority of a vessel wall including an annular wall portion (1) and a plate-wall portion (2) is formed of ceramic material such as silicon nitride, for example. To bond the plural wall members together, bonding faces having a surface flatness of not more than 1 .mu.m are prepared thereon, and then a ceramic powder bonding substance with an average particle diameter of not more than 1 .mu.m is interposed between adjacent bonding faces and subjected to heating. Because the generation of gas, such as hydrogen, from the wall of the ceramic vessel is reduced, extremely high vacuum can be generated and maintained in the interior of the vacuum vessel. Also, because the wall of the vacuum vessel has a high permeability with respect to a magnetic field and an electric field, the vacuum vessel can be used as a vessel in a particle accelerator that allows the high precision control of charged particles therein by means of an electromagnetic field.