The determination of the elasto⁃plastic critical point is very important for the study of the rough surface contact problem.In order to solve the shortcomings of the existing M⁃B model elasto⁃plastic critical point determination method

the characterization value is unmeasurable and difficult to apply.Based on the basic model of fractal theory

the distribution function and probability distribution density of asperity truncated area were obtained by means of mathematical statistics.Combined with the ideal elastic and plastic contact models of Hertzian contact

the normal force model in the process of plane⁃plane contact with fractal characteristics was obtained.Based on the difference between the actual contact area and the cut⁃off area during plastic deformation

a correction factor was proposed

and a method for determining the elasto⁃plastic critical point with the critical normal force as the characterization quantity was finally obtained.The new method takes the normal force as the characterization quantity and needs to be obtained through calibration experiments

which is more operational and credible.