The hypothetical model of ball lightning first suggested by P. L. Kapitza [Doklady Akad. Nauk S.S.S.R.101, No. 2, 245 (1955)] is considered in some detail in an attempt to uncover evidence which will substantiate or contradict the theory. Observers' reports of the phenomenon are summarized briefly. Pro and con arguments concerning Kapitza's scheme are given. A theoretical model in an ideal environment is examined. The radio‐frequency field suggested by Kapitza is considered, and the interference effects resulting from the reflection of a discrete band spectrum of linearly polarized waves from a perfect reflector are presented. The gaseous discharge is discussed, under the assumption that the ball lightning phenomenon is analogous to a point‐to‐plane corona discharge. It is determined that, given a sufficiently intense electric field, a horizontal discharge along one of the electric field antinodes, suggestive of horizontal lightning, can result. It is concluded that this exploratory work supports Kapitza's hypothesis, but that much more must be done before the theory is fully substantiated.