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Ionic electro-active polymers (EAP) are able to deform under the action of an electric field, which confers them many applications as sensor, actuator or energy recovery.An ionic metal-polymer composite (IPMC) consists in an ionic polymer film coated on both sides with a thin layer of metallic electrodes. The polymer is saturated with water, which results in its quasi complete dissociation : negative ions remain bound to the polymer backbone, which can be considered as a porous medium, and small cations are released in water. When an electric field orthogonal to the strip is applied, the cations move towards the negative electrode and carry solvent away by osmosis, causing the bending of the strip.We had previously established the conservation laws and the constitutive equations of this material. This model has been applied to the case of a cantilevered EAP strip subjected to a continuous voltage between its two faces (static case). Since the amplitude of the bending is large, the applied forces and the deflection are calculated using a beam model in large displacements. We also studied the case of a blocking force preventing the free end from moving. The material permittivity may increase with cations concentration, so we have compared several permittivity models : constant, linear and affine functions.Numerical simulations were performed in the case of Nafion. The resolution of the equations system enabled us to draw the profiles of various quantities (cations concentration, electric potential and induction, pressure), which drastically vary near the electrodes. The tip displacement and blocking force values obtained fit well the experimental data published in the literature. We also studied the influence of the strip geometry, which is identical for the three models. On the contrary, the variations of these two quantities with the imposed electric potential depend on the chosen permittivity model, which allows to discriminate them.