Abstract: The invention relates to a method of burnisning for the purpose of imparting surface compression stresses to metal parts. The surface state of the region of the part that is to be burnished is measured initially, and the width of the disk to be used in the burnishing is deduced therefrom. Thereafter, the disk selected in this way is installed on a tool carrier, at the end of an associated flexure bar. Once installed in this way the disk is pressed against the part to exert a predetermined force thereon as a function of the desired surface compression stresses. Finally, burnishing proper of the part is performed using the disk. The burnishing method of the invention is particularly advantageous for use with light alloy wheels, e.g. wheels made of magnesium or of aluminum alloy.