Flexibility　is　more　sensitive　to　structural　damage　than　frequency　or　mode.　Curvature　matrix　of　change　in　flexibility　is　presented　as　a　new　index　of　nondestructive　damage　detection,　which　is　derived　from　change　in　structural　flexibilities　calculated　from　before　damaging　and　after　damaging　by　means　of　difference　calculation　twice,　firstly　to　columns,　and　then　to　rows.　Therefore　a　new　indicator　called　as　delta　Flexibility　Curvature　Matrix　Diagonal　(delta　FCMD)　is　constructed　from　the　principal　diagonal　elements　based　on　curvature　matrix　of　change　in　flexibility.　The　numerical　simulation　examples　indicate　that　the　damage　location　and　severity　in　structures,　with　single　damage,　multiple　ones,　slight　ones　and　ones　at　the　supports,　can　be　detected　efficiently　for　a　cantilever　beam,　a　fixed　supported　beam,　a　simply　supported　beams　and　so　on　by　the　indicator　of　delta　FCMD　depending　on　only　a　few　of　lower　order　modes.