Abstract: Running in is the essential process before new machines put into operation,and itbrings the obivious changes of the surface topography of friction pairs.So it is necessary to studyhow to evaluate the topography of running-in surface. In fact ,the running-in is a process, that thesurface topography changes gradually from the initial state to the state of coinciding each other , sothe parameters of the surface topography of the friction pair after running -in have interrelation.This paper puts forward the method of evaluating running-in by mutul correlation structurefunction. This method has the advantages that can reflect the topography of two surfacessimultaneously, and can reflect sensitively the feature of the surface topography,and can considerseparately the peaks and the ralleys of the surface profile and so on. The theoretieal study and thepractical application have shown that the mutul correlation structure function is the optimumparameter of topography for evaluating running- in surfaces,and it can be considered as the basiccriterion of running-in.