Abstract: Running in process is indispensable before starting the normal operation of new machines. A proper running in process can prevent damage to machine components caused by scuffing in the early stages and so can significantly increase their service life. Based on the fractal characterization of worn surfaces, classical contact mechanics, and wear theory, a fractal model for predicting wear during the running in process was developed. The wear depth rate of Cu Zn pin sliding against AISI 1045 steel disc in the running in stage was determined with a pin on disc friction and wear tester and compared with the calculated one based on the fractal model. It has been found that the two conform well to each other. Thus the suggested fractal model can be used to predict the wear behavior of materials in the running in stage.