Simulating and modelling electric field dynamics in the insulation of medium- and high-voltage DC electrical systems is needed to support insulation design optimization and to evaluate the impact of voltage transients on ageing mechanisms and insulation reliability. In order to perform accurate simulations, appropriate physical models must be adopted for the insulating material properties, particularly conductivity, which drives the electric field in a steady-state condition and contributes to determining the field behavior during voltage and load transients. In order to model insulation conductivity, polarization, and conduction, mechanisms must be inferred through charging and discharging current measurements, generally performed at different values of electric field and temperatures in flat specimens of the material under study. In general, both mechanisms are present, but one of them may be predominant with respect to the other depending on type of material. In this paper, we showed that models based on predominant polarization mechanisms were suitable to describe impregnated paper, but not polymers used for HV and MV DC insulation. In the latter case, indeed, trapping–detrapping and conduction phenomena were predominant compared to polarization, thus conductivity models had to be considered, in addition to or as a replacement of the polarization model, in order to carry out proper electric field simulations.