Transient and steady state currents in polyethylene, under low and high dc voltages, are studied. In fact, a bipolar transport physical model is developed in order to characterize the space charge dynamics within an additive-free polyethylene film, under trapping and recombination mechanisms. The numerical computational models, used for the bipolar transport of carriers, are applied to the Poisson's, the continuity and the transport equations with the appropriate physical conditions. The principal and the new numerical results are calculated especially when high dc voltages are applied. Indeed, the net charge density numerical profiles show the appearance of the space charge packets that are revealed for the first time in numerical modelling although they have long been reported in experimental works. These space charge packets induce some new aspects on the external transient current evolutions, produce the oscillations of the conduction and the displacement current before the steady state, and generate a conduction regime that is dominated by the interface electrode-insulator. These numerical results are consistent with those reported in some experimental works. However, under low dc voltage the space charge packets disappear and the space charge limited current aspect appears on the external current profile.