A theory of cylindrical domains is presented for cases of a single domain in a plate of finite extent and of many domains scattered at random in a plate of infinite extent in the plane. Force and stability functions are determined for both cases. New unexpected solutions showing stability without a bias field, as well as those, for which the bias field must be directed in compliance with the magnetization in the cylindrical domain, are obtained. It is proved that the neglect of finite plate dimensions, as well as of the interaction between domains, is the cause of the apparent dependence of energy density of the domain wall on the bias field as stated in other reports. Theoretical considerations are proved by the experiments on the domain structure carried out on YFeO 3 orthoferrite.