We have clearly investigated with respect to the survival of the insulator at cryogenic temperature under the electrical stress. The breakdown and voltage-time characteristics of turn-to-turn models for point contact geometry and surface contact geometry using copper multi wrapped with polyimide film for an HTS transformer were investigated under AC and impulse voltage at 77 K. Polyimide film (Kapton) 0.025 mm thick is used for multi wrapping of the electrode. As expected, the breakdown voltages for the surface contact geometry are lower than that of the point contact geometry, because the contact area of the surface contact geometry is lager than that of the point contact geometry. The time to breakdown t50 decreases as the applied voltage is increased, and the lifetime indices increase slightly as the number of layers is increased. The electric field amplitude at the position where breakdown occurs is about 80 % of the maximum electric field value. The relationship between survival probability and the electrical stress at cryogenic temperature was evident.