Mechanical modeling of RF MEMS switches is important for performance optimization and device reliability. 1-D, 2-D, and 3-D linear analytical models have been proposed to analyze the electrostatic pull-in of a fixed-fixed beam at small deflection. However, most RF MEMS switch structures work at large deflection range. In this paper, 1-D, 2-D, and 3-D nonlinear analytical models suitable for large structural deflection are developed in a generalized form. In some practical applications, finite element models are required to account for the effects of all the design parameters: switch geometry, non-uniform state of residual stress, temperature and etc. A 3-D finite element model between structural, electrical and thermal domains is developed. This 3-D model is applicable to the design of all types of electrostatic actuators, though that of a capacitive coupling switch was examined.