The　micro-nanoscopic　morphology　of　the　contact　surfaces　directly　affects　the　tribological　behavior　between　the　contact　surfaces.　In　this　paper,　a　single　crystal　copper　substrate　with　nano　rough　surfaces　is　characterized　based　on　the　fractal　theory,　and　the　nano　rough　contact　model　which　could　exist　stably　at　room　temperature　(298　K)　is　established.　The　contact　behavior　between　rigid　plane　and　elasto-plastic　rough　substrate　is　analyzed.　It　is　found　that　only　a　few　higher　asperities　enter　the　contact　area　at　the　initial　contact　stage,　causing　large　fluctuations　in　contact　force.　However,　due　to　the　small　interaction　between　the　asperities,　the　contact　area　is　approximately　linear　with　the　contact　force.　If　the　ratio　of　real　contact　area　to　nominal　contact　area　is　greater　than　17%,　the　contact　force　and　contact　area　both　increase　with　the　increase　of　indentation　depth,　but　the　contact　area-contact　force　curve　deviates　from　the　linear　relationship　gradually　due　to　the　intensification　of　material　deformation　and　the　interaction　between　asperities.　©　2019　Taylor　&　Francis　Group,　LLC.