Abstract <p>The continuum and discrete charge transport models in the dielectric layer of a memristor for single charged traps taking into account the electric field from localized charges were developed. The probability rates of charge carrier hopping between traps, electron injection from the electrode to the nearest trap, and electron extraction from the nearest trap into the electrode were calculated using a model of phonon-coupled traps. It is shown that in weak external electric fields, the shielding effect of the electric field by localized charge carriers is significant, leading to incomplete filling of traps near the electrodes. It is found that for a moderate number of traps, the results obtained within the continuous model are very close to those obtained within the discrete model, but require greater computational power. The developed charge transport models were verified using experimental current–voltage curves for the high-resistance state of the TaN/HfO_<i>x</i>/Ni memristor (<i>x</i> ≈ 1.8), measured in the temperature range 200 to 350 K.</p>