To describe the deformation dynamics of polyelectrolyte gel, we formulate the electrostress diffusion coupling model. The model describes the interplay of the deformation of gel, permeation of water, and the transport of ions. The model gives a microscopic expression for the Onsager coefficient and allows us to discuss the effect of ionic radius. The model is then applied to the bending dynamics of a thin strip of ionic gels under stepwise application of electric field. The model qualitatively explains the relaxation behavior of an ionic gel (Nafion 117) for various kinds of ions including large counterions such as TEA(+) (tetraethylammonium).