For　second-order　problems,　where　the　behavior　is　described　by　second-order　partial　differential　equations,　the　numerical　manifold　method　(NMM)　has　gained　great　success.　Because　of　difficulties　in　the　construction　of　the　H-2-regular　Lagrangian　partition　of　unity　subordinate　to　the　finite　element　cover;　however,　few　applications　of　the　NMM　have　been　found　to　fourth-order　problems　such　as　Kirchhoff＇s　thin　plate　problems.　Parallel　to　the　finite　element　methods,　this　study　constructs　the　numerical　manifold　space　of　the　Hermitian　form　to　solve　fourth-order　problems.　From　the　minimum　potential　principle,　meanwhile,　the　mixed　primal　formulation　and　the　penalized　formulation　fitted　to　the　NMM　for　Kirchhoff＇s　thin　plate　problems　are　derived.　The　typical　examples　indicate　that　by　the　proposed　procedures,　even　those　earliest　developed　elements　in　the　finite　element　history,　such　as　Zienkiewicz＇s　plate　element,　regain　their　vigor.　Copyright　(C)　2013　John　Wiley　&　Sons,　Ltd.