An elastic support assembly for an electric power steering apparatus in which a worm shaft is supported movably in a rotation axis direction through the elastic support assembly includes: a pair of first and second members relatively moving in the rotation axis direction according to a movement of the worm shaft; an elastic body provided between the first and second members in the rotation axis direction; and a cover which covers an outer periphery part of the elastic body from a radial direction of the worm shaft and is connected to the first member.