The trap-assisted electron tunneling in thin insulators has been modeled to explain the apparition of plateaus in the current-voltage characteristics of some existing experimental data. As a consequence of the electron tight confinement in the trap, the charge therein has a steplike variation with the voltage increase, a feature that further translates into wide plateaus of the current-voltage diagrams, in accordance with some experimental data. The temperature dependence of these diagrams has been included into the model and compares well with the experimental evidence. The possibility of quantitatively comparing the model computations with the measured data opens useful insight into trap's physical properties such as spatial extent or energy depth.