Field asymmetric waveform ion mobility spectrometry (FAIMS) is rapidly gaining acceptance as a robust, versatile tool for post-ionization separations prior to mass-spectrometric analyses. The separation is based on differences between ion mobilities at high and low electric fields, and proceeds at atmospheric pressure. Two major advantages of FAIMS over condensed-phase separations are its high speed and an ion focusing effect that often improves sensitivity. While selected aspects of FAIMS performance are understood empirically, no physical model rationalizing the resolving power and sensitivity of the method and revealing their dependence on instrumental variables has existed. Here we present a first-principles computational treatment capable of simulating the FAIMS analyzer for virtually any geometry (including the known cylindrical and planar designs) and arbitrary operational parameters. The approach involves propagating an ensemble of ion trajectories through the device in real time under the influence of applied asymmetric potential, diffusional motion incorporating the high-field and anisotropic phenomena, and mutual Coulomb repulsion of ionic charges. Calculations for both resolution and sensitivity are validated by excellent agreement with measurements in different FAIMS modes for ions representing diverse types and analyte classes.