We develop a thermodynamic model of electrostriction for elastic dielectrics capable of large deformation. The model reproduces the classical equations of state for dielectrics at small deformation, but shows that some electrostrictive effects negligible at small deformation may become pronounced at large deformation. The model is then specialized to account for recent experiments with an elastomer, where the electric displacement is linear in the electric field when the strain of the elastomer is held fixed, but the permittivity changes appreciably when the strain changes. Our model couples this quasilinear dielectric behavior with nonlinear elastic behavior. We explore the consequence of the model by deriving conditions under which the deformation-dependent permittivity suppresses electromechanical instability. © 2008 American Institute of Physics.