Abstract　The　natural　frequencies　of　cracked　cantilever　beams　with　an　auxiliary　mass　are　derived　theoretically　in　the　present　work.　The　transverse　deflections　of　cracked　beams　are　constructed　by　adding　a　polynomial　function　in　representation　of　the　effects　of　a　crack　to　the　polynomial　function　describing　the　response　of　an　intact　beam.　The　analytical　formulation　of　the　distribution　of　natural　frequencies　due　to　auxiliary　mass　over　the　beam　is　obtained.　The　natural　frequencies　of　the　mass-beam　system　change　due　to　the　roving　of　the　mass　along　the　cracked　beam,　which　is　called　the　natural　frequencies　curve　(NFC).　The　NFC　obtained　using　the　theoretical　formulation　has　good　agreement　with　the　one　using　the　finite　element　method　(FEM).　In　addition,　because　the　NFC　contains　defect　information　of　the　beam,　the　damage　on　the　beam　can　be　easily　identified　using　stationary　wavelet　transform　(SWT).　Finally,　the　influence　of　defect　depth　and　defect　location　on　the　natural　frequency　of　the　mass-beam　system　is　considered　using　the　analytical　formulation.　The　results　demonstrate　the　reliability　of　the　theoretical　derivation　and　the　accuracy　of　the　damage　identification.　©　2016,　Editorial　Department　Chinese　Journal　of　Solid　Mechanics.　All　right　reserved.