A method for cold expansion of a hole formed in a work piece. The method comprises providing a body comprising at least a cylindrically shaped part having an inner hole in axial direction of the body. The body further comprises along its circumferential direction a plurality of members which are movable in radial direction of the body, such that the outer diameter of the cylindrical part of the body can be changed. The method comprises introducing the body into the hole formed in the work piece; inserting a core into the inner hole of the cylindrically shaped part, wherein at least one of the core or the inner hole comprises a portion having changing diameter and the inner hole and the core get into contact with respect to each other upon insertion of the core, such that in dependency of the insertion depth of the core into the inner hole in axial direction the members move in radial direction outwardly and the outer diameter of the cylindrical part of the body increases and, accordingly, acts on the inner circumference of the hole formed in the work piece so that a boundary zone of the hole is compressed, which leads to a compression or hardening and, accordingly, to the introduction of compressive stress in the boundary zone. The inner hole and the core have a polygonal cross section in a direction perpendicular to the longitudinal axis, and the hole formed in the work piece is expanded over the entire thickness of the work piece in which the hole is formed.