Microsystems are very small sensors and actuators, manufactured with the same technology as computer chips. Well known applications of these machines are the acceleration sensors in the Wii game console and the iPhone. At the micrometer length scales of microsystems the physical forces behave different when compared to devices operating in the scale of meters: physical fields are highly coupled. One of the more useful couplings is the strong coupling between electrostatic forces and mechanical deformation. Only recently computers became fast enough to model these devices using methods that actually discretize the partial differential equations that describe those electro-mechanical problems. Therefore this dissertation is concerned with developing and improving those finite element based methods. A special attention is given to analyzing the effect of fabrication and material uncertainties on the crucial results that models provide.