A　2-D　sliding　model　of　micro-scale　was　established　between　two　rough　surfaces　exhibiting　fractal　behavior,　and　the　stress　and　strain　was　discussed　by　using　the　finite　element　analysis.　A　pair　of　asperities　was　analyzed　take　into　account　elastic-　plastic　material　properties　with　material　failure.　The　transient　stress/strain　distribution　of　the　rough　solid　was　presented.　The　numerical　results　showed　that　the　equivalent　plastic　strain　versus　different　depth　which　at　different　locations　showed　different　laws.　Failure　began　beneath　the　surface　at　the　region　of　highest　plastic　strain.　A　shear　stress　zone　exited　at　a　certain　depth　from　the　contact　surface　in　the　rear　of　the　contact　asperity.　This　shear　stress　zone　on　the　one　hand　prevented　the　crack　from　extending　along　the　depth　direction,　on　the　other　hand,　prompted　the　crack　along　an　extension　of　the　parallel　to　the　direction　of　the　friction　surface　crack　growth　and　leads　to　final　fracture.