Contact　interaction　of　two　bodies　can　be　modeled　using　the　penalty　function　approach　while　its　accuracy　and　robustness　are　directly　associated　with　the　geometry　of　contact　bodies.　Particularly,　in　the　research　fields　of　rock　mechanics,　we　need　to　treat　polygonal　shapes　such　as　mineral　grains/particles　at　a　mesoscale　and　rock　blocks　at　a　macroscale.　The　irregular　shapes　(e.g.,　polygons　with　small　angles　or　small　edges)　pose　challenges　to　traditional　contact　solution　approach　in　terms　of　algorithmic　robustness　and　complexity.　This　paper　proposed　a　robust　potential-based　penalty　function　approach　to　solve　contact　of　polygonal　particles/block.　An　improved　potential　function　is　proposed　considering　irregular　polygonal　shapes.　A　contact　detection　procedure　based　on　the　entrance　block　concept　is　presented,　followed　by　a　numerical　integral　algorithm　to　compute　the　contact　force.　The　proposed　contact　detection　approach　is　implemented　into　discontinuous　deformation　analysis　with　an　explicit　formulation.　The　accuracy　and　robustness　of　the　proposed　contact　detection　approach　are　verified　by　benchmarking　examples.　The　potential　of　the　proposed　approach　in　analysis　of　kinetic　behavior　of　complex　polygonal　block　systems　is　shown　by　two　application　examples.　It　can　be　applied　in　any　discontinuous　computation　models　using　stepwise　contact　force-based　solution　procedures.