This paper presents a new equivalent-circuit model of SiBARs, derived in a mathematically rigorous way from the physics equations governing the behavior of the device. The model is parametric, that is, the model component values can be computed directly from the dimensions of the resonator and the properties of the material. The model also accounts fully, accurately and automatically for aspects of the device behavior that arise from the interaction of multiple physics domain: the shift in the resonance frequency with the polarization voltage (“spring softening”), the effect of the polarization voltage and gap size on the insertion loss, and the reduction in the resonator loaded Q as the polarization voltage is increased. In contrast, those effects are not automatically accounted for by other models, such as mass-spring combinations. Finally, the model described is load- and source-independent, and thus it reproduces accurately the behavior of the device itself, regardless of the type and characteristics of the surrounding circuitry.