The　numerical　manifold　method　(NMM)　has　been　employed　to　solve　many　types　of　engineering　problems.　To　improve　accuracy　of　the　traditional　NMM,　a　second-order　NMM　with　six-node　triangular　mesh　was　recently　proposed.　This　second-order　NMM　is　further　applied　for　structural　dynamic　problems　in　this　study.　In　order　to　reduce　time　consumption　in　solving　large　scale　simultaneous　algebraic　equations,　a　mass　lumping　scheme　which　is　suitable　for　the　second-order　NMM　is　proposed.　A　series　of　numerical　examples　show　that　natural　frequencies　of　structures　assessed　from　the　proposed　lumped　mass　matrix　(LMM)　are　more　accurate　than　those　from　the　consistent　mass　matrix　(CMM).　In　addition,　even　in　the　implicit　time　integration　scheme　to　predict　dynamic　responses　of　structures,　the　CMM　can　be　replaced　by　the　proposed　LMM　without　losing　accuracy.　(C)　2018　Elsevier　Ltd.　All　rights　reserved.