Ionic polymer metal composites (IPMCs) are active materials that exhibit a bidirectional electromechanical coupling. An IPMC is an electrolytic polymer membrane that is plated by two metallic electrodes. A voltage difference across the electrodes generates structural deformations; and, conversely, a mechanical deformation yields a voltage difference across the electrodes. In this paper, we develop a physics-based model for the sensing and actuation of IPMCs undergoing small deformations. The model describes a variety of phenomena taking place in an IPMC, including counterions, solvent, and polymer motions; electric dipole generation; osmotic effects; boundary layer formation; polymer swelling; and local charge imbalances. We specialize the model to the analysis of linear static deformations of a thin and flat IPMC, for which we derive a plate-like model. The reduced-order linear plate-like model is derived by using the principle of virtual work and a parallel-plate approximation for the electrostatic field inside the IPMC. The proposed plate-like model is equivalent to traditional plate models for moderately thin piezoelectric bimorph plates. The constitutive parameters of the plate-like model are expressed in terms of fundamental IPMC physical quantities, such as polymer hydration level, IPMC dielectric constant, polymer and electrode dimensions and elastic properties, and solute concentration. We validate the reduced-order model by comparing its predictions with available experimental data on mechanical stiffness, electric capacitance, and sensing and actuation capacity of water-hydrated Nafion in Na⁺ form. The model predictions are in close agreement with experimental findings. The model provides new insights into the design and optimization of IPMCs and into the role of the IPMC electric capacitance on electromechanical performance. More specifically, we show that the IPMC capacitance is largely independent of the IPMC thickness and highly correlated to the thickness of the boundary layers formed by the counterion species in the vicinity of the electrodes. Further, we analytically show that the capacitance strongly influences the sensing and actuation effectiveness of IPMCs.