简介：Basedonthevariationaltheory,awavelet-basednumericalmethodisdevelopedtocalculatethedefectstatesofacousticwavesintwo-dimensionalphononiccrystalswithpointandlinedefects.Thesupercelltechniqueisapplied.Byexpandingthedisplacementfieldandthematerialconstants(massdensityandelasticstiffness)inperiodicwavelets,theexplicitformula-tionsofaneigenvalueproblemfortheplaneharmonicbulkwavesinsuchaphononicstructurearederived.Thepointandlinedefectstatesinsolid-liquidandsolid-solidsystemsarecalcu-lated.Comparisonsofthepresentresultswiththosemeasuredexperimentallyorthosefromtheplanewaveexpansionmethodshowthatthepresentmethodcanyieldaccurateresultswithfasterconvergenceandlesscomputingtime.