PROBLEM TO BE SOLVED: To provide a sleeve for axial-diameter-enlarging work, in which a stick workpiece can be subjected to the axial-diameter-enlarging work to form an enlarged part, and at the same time, an end of the workpiece is also subjected to the work; and to provide an axial-diameter-enlarging work apparatus, and an axial-diameter-enlarging work employing the same.SOLUTION: The sleeve 1 for the axial-diameter-enlarging work holds the end of the workpiece 2, when the metal workpiece 2 is pressurized in a direction where the workpiece is reduced along an axis A and energy is applied in a direction crossing the axis A to enlarge any part of the workpiece 2. The sleeve includes: a hole 5a to which the workpiece 2 is inserted; and one or more reduced diameter parts 13 formed at at least part of an inner peripheral surface on any cross section of the hole 5a and formed inside of an outer diameter of the workpiece 2 inserted in the hole 5a.
