Irregular　polygon　shapes　(eg,　with　small　edges　or　small　angles)　are　usually　encountered　in　the　contact　simulation　of　discrete　block　systems.　Treatment　of　irregular　polygons　in　contact　detection　process　has　critical　effects　on　the　robustness　and　efficiency　of　the　discontinuous　computation　approach.　The　present　work　proposes　a　cover-based　strategy　to　detect　and　solve　contacts　of　irregular　convex　polygons　in　a　robust　and　efficient　way.　Contact　constraints　of　two　polygons　are　represented　by　vertex-edge　and　edge-vertex　contact　covers　in　2D.　Two　loops,　namely　vertex-edge　loop　and　edge-vertex　loop,　and　two　filter　criteria,　namely　the　entrance　filter　criterion　and　the　distance　filter　criterion,　are　used　to　establish　the　potential　contact　cover　list　of　two　neighbor　polygons.　The　initial　active　and　closed　contact　covers　are　chosen　based　on　block　configuration　at　the　beginning　of　the　step　and　they　are　then　updated　in　the　open-close　iteration　process　using　proposed　criteria.　This　strategy　is　implemented　in　discontinuous　deformation　analysis.　The　robustness　of　the　proposed　cover-based　approach　and　the　conventional　type-based　approach　in　handling　contact　of　irregular　blocks　is　verified　first.　Then,　the　contact　analysis　efficiency　of　the　cover-based　approach　with　different　contact　tolerances　is　evaluated.　This　cover-based　method　can　be　extended　to　3D　case　for　efficient　and　robust　contact　analysis　of　irregular　polyhedral　blocks.