To provide a graphite electrode excellent in thermal shock resistance by accurately grasping estimation factors of thermal shock resistance of a graphite electrode for steel making.

The thermal shock resistant graphite electrode used for an arc furnace for steel making, has a thermal shock fracture toughness index of 0.8×10-2 to 1.6×10-2 mm/sec expressed in a formula: K=L/H, (where, K denotes a thermal shock fracture toughness index, L denotes an opening displacement volume (mm) at a breaking point of a notched part obtained from a thermal shock test of carrying out an arc heating at a power of 50V and 2kA of a center part of a diameter of 40 mm, with the notched part of a length of 30 mm fitted at a square plate of 250×250×50 mm cut out vertically in an extrusion molding direction from the center part of the graphite electrode from an outer periphery edge of its longer sides, and H denotes an arc heating time (sec) up to a breaking point of the notched part.).