The　interaction　between　adjacent　asperities　is　a　typical　characteristic　of　the　grinding　process　and　plays　an　important　role　in　the　material　removal　mechanism.　Therefore,　in　order　to　systematically　investigate　the　formation　mechanism　of　the　subsurface　damage,　a　precision　grinding　contact　model　between　the　diamond　particle　and　optical　glass　with　adjacent　asperities　is　proposed　in　our　research.　The　initiation　and　propagation　mechanism　of　median/lateral　cracks　under　residual　stress,　the　propagation　rules　of　the　stress　waves　on　the　subsurface,　and　the　interaction　between　the　subsurface　damage　under　stress　superposition　effect　are　fully　investigated　by　a　theoretical　analysis　and　finite　element　simulation.　The　simulation　results　of　the　precision　grinding　model　are　verified　by　experiments,　which　show　that　the　proposed　numerical　analysis　model　is　reasonable　and　the　finite　element　analysis　process　is　feasible.　©　2019　by　the　authors.