Microelectromechanical systems (MEMS) combine high levels sensitivity and multifunctionality with small size and low power consumption. The major prime mover for MEMS industry in the past has been automobiles whereas consumer electronics (E.g. iPhones and Nintendo Wii) is the most important sector for growth now. With new focus on small scale energy harvesting from ambient vibration and air flow, MEMS have definitely entered a new generation. A significant factor propelling design and manufacturing is the need for reliable and robust computational tools. The basic skeleton of MEMS still remain suspended or anchored beams and plates actuated by electrical, electrostatic, thermal, magnetic or photonic mechanisms. This dissertation describes the simulation of coupled dynamics of thin MEMS actuated electrostatically and vibrating in a fluid medium. Although, only micro-beams are addressed here, the computational structure developed here can be directly used to address other forms of actuation or medium. A fully Lagrangian approach is developed to couple the electrostatic, fluidic and mechanical problem which is then solved using Newton's method. This approach eliminates the problems arising from remeshing and computing of derivatives of integrals over changing domain shapes. The mechanical problem is solved using finite element method (FEM) whereas the fluidic and electrostatic problems are tackled using the boundary element method (BEM). Severe numerical issues arise when dealing with very thin microstruc- tures (very high aspect ratio) for the BEM problem due to nearly singular integrals. A special BEM which addresses these problems has been developed for both the electrostatic and the fluidic problem. A singularity of mathematical nature arises at the free edge for the electrostatic BEM problem when dealing with cantilevers. This problem is solved by incorporating a singular element formulation for the electrostatic BEM. The resulting solution is compared with the case of simple extrapolation for some typical performance parameters. Finally, several possible extensions of current work like adapting the algorithm for nanoelectromechanical systems (NEMS), computational acceleration using the fast multipole method (FMM) and quantifying uncertainty has been explained in the concluding chapter.