This paper focuses on the modeling methods of characteristics and parameters of the external surface structure of a tribological system, which is used in design of precision kinematic joint connection. Also, as part of this work, there were discussed research methods and the calculations of bifurcation components of a sliding friction during a tribological interaction. There were shown modelling methods of surface roughness structure by using an elastic element. For this purpose was proposed a rod of square section, that has fixed one end. With the proposed method were demonstrated dependences between the dynamic characteristics of the tribological interaction and external structural parameters of the friction surfaces.