Calculations of the electric field distribution in the electrode system in the form of a spherical concentric capacitor simulating a micro-tip on the cathode were performed under the action of a high-voltage pulse with a front steepness of about 1 GV/s and electron injection from the micro-tip. The penetration depth of the negative space charge (NSC) into the polymer was shown to be 0.2–0.3 μm during a 150–250 ns pulse front edge. Electrical overvoltages caused by the geometry of the electrode system and the accumulating NSC occurred in the NSC accumulation region at the pulse front edge. The field strength at the cathode decreased multiple times during the transition from the pulse front to its plateau in 100–200 ns.