The nanoscale structure of single-walled carbon nanotubes (SWCNTs) has unique properties. These nanostructured additives can induce unusual characteristic in many polymer matrix. In one of our recent experiments it was found that when adding SWCNTs into a polyimide (P1) matrix, friction becomes a function of the concentration of the additive. In this research, we analyze the behavior of the SWCNTs-PI nano composite using an approximation approach. We report that the frictional behavior of the nanocomposite is dominated by the elastic and plastic deformation through randomly dispersed SWCNTs under different loading conditions. At low concentration of SWCNTs, its elasticity dominates the properties of composite while at higher concentration, plastic behavior of tubes plays a major role in describing the properties of composite.