In this paper, the behavior of an electrochemical thin polymeric film sandwiched between porous electrodes and under input voltage (potentiostatic) conditions is numerically investigated. Thin polymeric membranes, such as Nafion, are widely used in micro-batteries and proton-exchange-membrane fuel cells. A three-dimensional continuum-based multi-field formulation for thin polymeric membranes is presented. The model is applied to configurations of the type electrode-membrane-electrode in order to represent the core of a characteristic electrochemical device. Various three-dimensional geometries are considered. The phenomena modeled within the polymeric membrane are (i) ion transport (chemical field) and (ii) electrical field. The field equations, i.e. the Poisson-Nernst-Planck equations, are determined by inserting the thermodynamically consistent constitutive equations within the balance equations of the electrochemical problem. Suitable initial and boundary conditions have to be imposed in order to solve the system of partial differential equations. In particular, the phenomena modeled at the membrane/electrode interface are (i) the electrochemical kinetics of the chemical reaction and (ii) the polarization effects. Time-dependent numerical simulations for potentiostatic conditions are performed within a finite element framework. It is shown that the presented fully coupled multi-field model reproduces, within a simulation framework, the behavior of electrochemical cells. In fact, the model is capable of well predicting the space and time evolution of the main electrochemical parameters as well as catching multi-dimensional effects. The presented model can be regarded as a starting point to develop further research concerning an electro-chemo-mechanical model in order to well understand the stress distribution which arises in polymeric membranes during operating conditions.