Theinteractionofanti-planeelasticSHwaveswithaperiodicarrayofinterfacecracksinamulti-layeredperiodicmediumisanalyzedinthispaper.AperfectperiodicstructurewithoutinterfacecracksisfirststudiedandthetransmissiondisplacementcoefficientisobtainedbasedonthetransfermatrixmethodinconjunctionwiththeBloch-Floquettheorem.Thisisthengeneralizedtoasingleandperiodicdistributionofcracksatthecenterinterfaceandtheresultiscomparedwiththatofperfectperiodiccaseswithoutinterfacecracks.Thedependenceofthetransmissiondisplacementcoefficientonthefrequencyoftheincidentwave,theinfluencesofmaterialcombination,crackconfigurationandincidentanglearediscussedindetail.Comparedwiththecorrespondingperfectperiodicstructurewithoutinterfacecracks,anewphenomenonisfoundintheperiodiclayeredsystemwithasingleandperiodicarrayofinterfacecracks.