Abstract: The burnishing method and apparatus for implementing the method of the present invention utilizes a single-point burnishing process to provide deep compression with a minimal amount of cold working and surface hardening. In particular, the area to be burnished along the surface of a workpiece is defined and a freely rotating burnishing ball is forced against the surface of the workpiece to produce a zone of deformation having a deep layer of compression within the surface. The burnishing ball is then rolled over the surface in a substantially nonoverlapping pattern. A preferred embodiment of the burnishing apparatus for implementing the burnishing method comprises a socket having a tip member incorporating a ball seat, a burnishing ball disposed within the ball seat, a rod member integrally formed with the tip member; and a socket support for supporting the socket on a conventional tool holder.