We describe and demonstrate the capabilities of a new coupled-field simulator based on the industrial CAD platform TP2000 for the multidimensional numerical analysis of the operation of electro-mechanical microdevices. The coupling of the finite element and the boundary element methods for the mechanical and the electrical domain, respectively, makes the simulation tool particularly suited for microdevices where movable parts are deflected, displaced, or rotated by electrostatic forces. A homotopy method is employed for unstable operating points, which inherently occur in any electrostatically driven microdevice. Using this method, the stable, as well as the unstable regions of the operating area of a device can be calculated in the same way with equal accuracy and robustness. As illustrative examples, we study the fully coupled electro-mechanical behavior of a deflectable micromirror, a membrane drive and an interdigitated comb structure.