InthispaperwegiveaconvergencetheoremfornonC^0nonconformingfiniteelementtosolvetheellipticfourthordersingularperturbationproblem.Twosuchkindofelements,anineparametertriangularelementandatwelveparameterrectangularelementbothwithdoublesetparameters,arepresented.Theconvergenceandnumericalresultsofthetwoelementsaregiven.