It is very difficult to establish high-fidelity model for self-actuation failure threshold power of switch when considering the fringing field effect of the electric field distribution of the capacitive RF MEMS(Radio-Frequency Micro-Electro-Mechanical System) switch membrane. Therefore, in order to characterize the intensity of the fringing field effect of the electric field distribution on the membrane, the Figure of Merit(FoM) is constructed by using the ratio between the area of the switch membrane subjected to RF power(ARF) and the facing area(A) (which is between the membrane and the transmission line). The three-dimensional electromagnetic model of self-actuation failure of the switch is constructed by using the HFSS(High Frequency Structure Simulator) software. For a case of a common configuration of the switch, the distribution of fringing electric field of membrane under a variety of RF signal powers (Pin) and with different air gaps of the switch(g0) are obtained through simulation. The comparison between the calculation of FoM and simulation results indicates that it is feasible to characterize the intensity of the fringing field effect of the electric field distribution of the membrane by using FoM(ARF/A).