The　study　of　the　size　effect　was　one　of　the　most　important　subjects　in　the　field　of　micro-forming.　To　investigate　the　stress　of　the　thin　sheet　in　the　bulging　test　with　the　second　order　size　effect,　a　constitutive　equation　considering　the　strain　gradient　hardening　was　proposed.　Based　on　the　equation,　the　stress　of　the　thin　sheet　during　the　bulging　test　was　calculated　by　the　finite　element　method.　The　bulging　tests　with　various　thicknesses　of　brass　sheets　and　radiuses　of　punching　balls　were　performed　to　verify　the　proposed　equation.　The　results　showed　that　the　constitutive　equation　could　capture　the　stress　variations,　while　the　simulation　using　the　constitutive　equation　from　the　conventional　theory　of　plasticity　showed　the　results　with　large　deviation　from　those　of　the　experiment.　It　was　found　that　the　stress　was　sensitive　to　the　thickness　of　the　sheet　and　the　radius　of　the　punching　ball　in　bulging　test　of　thin　brass　sheet.　The　bulging　of　the　thin　brass　sheet　with　a　thickness　below　ten　times　of　its　material　intrinsic　length　would　cause　the　generation　of　the　geometrically　necessary　dislocations,　which　induced　the　strain　gradient　hardening.　Besides　that,　the　decrement　of　the　punching　ball　radius　would　also　increase　the　inhomogeneous　deformation　and　enhance　the　strain　gradient　hardening　during　the　thin　sheet　bulging　process.　The　strain　gradient　hardening　during　the　thin　sheet　bulging　test　was　related　to　the　strain　of　the　sheet.　The　hardening　effect　of　the　strain　gradient　was　obvious　when　the　strain　was　small.　The　strain　gradient　hardening　should　be　considered　in　the　thin　sheet　bulging　test　with　the　second　order　size　effect.　©　Liang　et　al.