The general problem of configuration interactions for the excited states in ideal insulators is investigated by solving a difference equation which is derived in the same way as in the scattering problem. It is shown that the general picture of exciton falls into three categories: deep case, shallow case, and hydrogenic case, according to different conditions under which the difference equation is to be solved approximately. The structures of the bands of both the singlet and triplet excitons are investigated in these three cases, with particular emphasis on the deep case. The solution derived is intermediate between the “atomic” and “continuum” models hitherto proposed.