Computational energy minimization and free-energy minimization techniques have been used to study the structures and crystal properties of muscovite, phlogopite, and several octahedrally substituted phlogopite analogues. These simulations employ ionic potential models that include three-body O-Si-O bond-bending terms. The calculated structures of these micas are in acceptable agreement with experiment. Moreover, the elastic and dielectric constants and the acoustic phonon properties of muscovite are in close agreement with experiment, thereby demonstrating the applicability of the techniques and potential models to this class of material. The effects of divalent octahedral cation substitution on the structure of phlogopite are also studied.