Many　rectangular　plate　elements　developed　in　the　history　of　finite　element　method　(FEM)　have　displayed　excellent　numerical　properties,　yet　their　applications　have　been　limited　due　to　inability　to　conform　to　the　arbitrary　geometry　of　plates　and　shells.　Numerical　manifold　method　(NMM),　considered　to　be　a　generalization　of　FEM,　can　easily　solve　this　issue　by　viewing　a　mesh　made　up　of　rectangular　elements　as　mathematical　cover.　In　this　study,　ACM　element　(Adini　and　Clough　element　from　A.　Adini,　R.W.　Clough,　Analysis　of　plate　bending　by　the　finite　element　method,　University　of　California,　1960),　a　typical　rectangular　plate　element　is　first　integrated　in　the　framework　of　NMM.　Then,　vibration　analysis　of　arbitrary　shaped　thin　plates　is　conducted　employing　the　tailored　NMM.　Using　the　definition　of　integral　of　scalar　functions　on　manifolds,　we　developed　a　mathematically　rigorous　mass　lumping　scheme　for　creating　a　symmetric　and　positive　definite　lumped　mass　matrix　that　is　easy　to　inverse.　A　series　of　numerical　experiments　have　been　studied　and　analyzed,　including　free　and　forced　vibration　of　thin　plates　with　various　shapes,　validating　the　proposed　mass　lumping　scheme　can　supersede　the　consistent　mass　formulation　in　those　cases.　(C)　2018　Elsevier　Inc.　All　rights　reserved.