Three-dimensional　finite　element　modeling　of　the　contact　between　a　rigid　spherical　indenter　and　a　rough　surface　is　presented　when　considering　both　the　loading　and　unloading　phases.　The　relationships　among　the　indentation　load,　displacement,　contact　area,　and　mean　contact　pressure　for　both　loading　and　unloading　are　established　through　a　curve　fitting　using　sigmoid　logistic　and　power　law　functions.　The　contact　load　is　proportional　to　the　contact　area,　and　the　mean　contact　pressure　is　related　to　the　characteristic　stress,　which　is　dependent　on　the　material　properties.　The　residual　displacement　is　proportional　to　the　maximum　indentation　displacement.　A　proportional　relationship　also　exists　for　plastically　dissipated　energy　and　work　conducted　during　loading.　The　surface　roughness　results　in　an　effective　elastic　modulus　calculated　from　an　initial　unloading　stiffness　several　times　larger　than　the　true　value　of　elastic　modulus.　Nonetheless,　the　calculated　modulus　under　a　shallow　spherical　indentation　can　still　be　applied　for　a　relative　comparison.　©　2018,　The　author(s).