Featured Application Reduction and control of surface irregularities during the nanostructuring burnishing of elastic workpieces such as transmission shafts. Abstract Nanostructuring burnishing is an effective and mature process for enhancing the surface properties of metallic workpieces. Through severe mechanical deformation, nanostructuring burnishing forms a very hard and smooth surface layer that improves the wear resistance and other properties of the workpiece. This surface treatment requires careful control of process conditions, as the application of large forces and sliding velocities can easily damage the workpiece either through overheating or self-excited oscillation, resulting in an uneven surface. In this paper, we investigate one possible source of such instabilities, namely, unstable stick–slip motion in the sliding direction. When combined with the coupling of normal and tangential stresses through the von Mises yield criterion, the resulting fluctuations of the coefficient of friction can temporarily decrease the effective indentation hardness in the normal direction and thereby produce an uneven indentation track. A dynamical model based on this mechanism is investigated numerically, and the results are found to be in qualitative agreement with experimentally observed surface irregularities encountered in the burnishing of a long drive shaft. The influence of the local bending stiffness at various points along the shaft is also taken into account. Keywords: nanostructuring burnishing; surface enhancement; stick–slip; suppression of instabilities