In this paper we derive two models (a static and a dynamical model) based on the description of the electric potential in a biological cell in order to model the cell electropermeabili-zation. Existence and uniqueness results for each model are provided, and accurate numerical method to compute the solution is presented. We then present numerical results that corroborate the experimental results, justifying the validity of our modeling. We emphasize that our new models involve very few parameters, compared with the most achieved model but they describe the same qualitative results. Moreover our numerical resultsare quantitavely close to the experimental data.