The antennas for mobile communication handsets have become smaller in shape, which has degraded their electrical performance significantly. To obtain a small but high-performance handset, it is important to increase the antenna efficiency. The important parameter for such a purpose is the radiation efficiency which can be measured easily by the Wheeler method. This method is carried out based on the assumption that the input power is equal to the power loss if the antenna is covered with a cap of a size on the order of a radian sphere. However, unless this assumption holds, the computed Wheeler efficiency does not give accurate radiation efficiency. When the radiation efficiency is actually measured by the Wheeler method, the measured values often have a dip from the theoretical value. In this paper, the cap is approximated by wire grids and the Wheeler method is simulated on a computer. It is confirmed that the dip is not caused by the measurement method. It is shown that the cause derives from the invalidness of the presumption of the Wheeler method that the internal reactive electromagnetic field does not change when a cap is placed. It is shown also that the Wheeler method can be used sufficiently even if the size of the cap is larger than the radian sphere. The limit of application is studied.