PURPOSE: To apply a braking force to the relatively low position of a tail cord, and prevent the damage of the tail cord or the like, even when the upward overrun of a cage takes place.

CONSTITUTION: In an elevator tail cord damping device provided on the tower of an elevator to apply a braking force to the curved bottom of a tail cord 9 suspended between the tower and a cage, there is provided a cord 17 with one end connected to the tail cord 9, a cylindrical body 18 so housing the other end of the cord 17 as to be movable and mounted on the aforesaid elevator tower, and a counterweight 18 connected to the other end of the cord 17 for applying tension thereto. The aforesaid construction can be easily applied to an existing elevator without any need of a substantial modification.