Field computation problems with symmetrical boundaries often give difficulties like degenerate solutions [4] or singular matrices [6]. By considering all symmetry properties one can avoid these difficulties and at the same time strongly reduce the amount of computation and the storage requirement. A mathematical description of symmetries is introduced, Representation theory then gives a relation between geometrical symmetry and the symmetries of function spaces. A table showing the possible splitting into subspaces is given. Some concrete examples are described which show the application to finite elements and finite differences method, method of moments, point matching and image charge method.