In the performance of antenna measurements the antenna is usually placed over a large conducting screen. The assumption is then made that the measurements are in close agreement with those that would be obtained if the screen were of infinite size. Recent experimental work, however, indicates that the finiteness of the ground screen may influence the measurements to a considerable extent.It is therefore desirable to solve this problem theoretically in order to determine the extent of the change introduced by the use of a finite screen. This paper treats the problem of an antenna erected vertically in the center of a circular screen. An integral equation is obtained for the electric field in the plane of the screen, outside the screen. This equation is solved approximately by the use of a variational principle, and a formula is obtained for the change of antenna impedance as a function of the diameter of the screen. The formula may be used to give a simple and accurate estimate of the changes introduced by the use of a finite screen.