In former report, under the same title, which appeared about ten years ago, by the same author, we made an analytical study with regard to vibration of two circular cylinders which are immersed in a fluid region of infinite extent. Therein, the vibration was assumed to be of infinitesimally small magnitude. The present paper is the continuation of analytical study of the same problem, and here we treat the case of vibration of finite amplitudes. As before, we take the case of two dimensional problem about an ideal fluid. In the present study, (Part II), only main analytical formulae about this problem is given, more detailed account together with numerical example being to be given in subsequent paper.