A conductivity model for insulating oil and paper under the stress of high DC voltage is presented. It is based upon the different physical properties of the intrinsic and injected oil charge carriers. The model assumptions are translated into the PoissonNernst-Planck-equation by utilizing adequate boundary conditions for the electric field and the particle currents. Hence a tool is available, whose parameter base on the physical properties of the charge carriers such as mobility and diffusion coefficient. The dielectric properties such as nonlinear conductivity and the breakdown as its field strengh extrapolation are being explained.