It is well known that space charge accumulation in insulating materials constitutes the principal cause of dielectric breakdown. Though space charge measurements in polymeric materials have been extensively developed over the last two decades, modeling and simulation works have progressed slowly in this respect. In the present study, a model for bipolar charge transport, as a basis for studying breakdown phenomenon in low density polyethylene (LDPE), is presented. Indeed, we are especially interested in external current dynamic which is the witness of the sample post breakdown. Our results show the effect of the high dc applied voltage and the generation of the space charge packets on the apparition of the post breakdown of the insulator. In order for this effect to be revealed, the external current evolutions under low and high dc applied voltages before and at the breakdown are determined. Indeed, these evolutions show an abrupt increase that is observed when the charge packet aspect occurred in the sample under high dc applied voltage. This observed abrupt increase of the external current is attributed to post breakdown phenomenon. These results are obtained for the first time in modeling and show some aspects similar to those observed in some experimental works.