An ionic polymer-metal composite (IPMC) consisting of a thin Nafion sheet, platinum plated on both faces, undergoes large bending motion when an electric field is applied across its thickness. Conversely, a voltage is produced across its faces when it is suddenly bent. A micromechanical model is developed which accounts for the coupled ion transport, electric field, and elastic deformation to predict the response of the IPMC, qualitatively and quantitatively. First the basic 3D coupled field equations are presented, and then the results are applied to predict the response of a thin sheet of an IPMC. Central to our theory is the recognition that the interaction between an imbalanced charge density and the backbone polymer can be presented by an eigenstress field. The constitutive parameter connecting the eigenstress to the charge density is calculated directly using a single microstructural model for Nafion. The results are applied to predict the response of samples of IPMC, and good correlation with experimental data is obtained. Experiments show that the voltage induced by a sudden imposition of a curvature, it two orders of magnitude less than that required to produce the same curvature. The theory accurately predicts this result. The theory also shows the relative effects of different counter ions, e.g., sodium versus lithium, on the response of the composite to an applied voltage or a curvature.