Abstract: The character of asperity micro-displacements caused by a tangential load for perfect elastic or fully plastic contact materials was studied clearly by Fujimoto (2000). However, for most contacts of elastic-plastic materials, the above conditions cannot be satisfied. Here taken the Fujimoto model as the foundation and based on the Cattaneo & Mindlin theory, the relation between a contact friction and a micro-displacement under a tangential load for elastic-plastic materials is studied. At last, an example is given to verify the application of the theoretical method proposed.