In the former report, under the same title as the present one, the author has made analytical study about vibratory motion of two circular cylinders, which are immersed in fluid region of infinite extent. The fluid was taken to be an ideal fluid, and we treated the problem as a case of two-dimensional motion, two circular cylinders being of different radii. In the present Report IV, we examined the case in which one circular cylinder is of infinite radius, as a special case to previous study. Thus, we could show here, the case of motion of a circular cylinder, which is immersed in a fluid region which is bounded by a straight rigid wall of infinite extent. And, hereby, for the case of two-dimensional potential flow of an ideal fluid, amount of hydrodynamical force (Fx, Fy) acting on the circular cylinder was obtained. Some numerical examples about this hydrodynamical force, are also given.