The　numerical　manifold　method　(NMM)　has　been　applied　successfully　to　a　wide　variety　of　problems,　including　time-independent　exterior　problems,　where　problem　domains　are　unbounded.　However,　of　the　utmost　interest　and　significance　is　the　analysis　of　wave　propagation　in　unbounded　domains,　which　is　still　an　open　issue　because　it　is　far　more　difficult　than　time-independent　exterior　problems.　This　study　aims　to　fill　partly　this　gap　from　the　prospective　of　NMM.　A　new　type　of　infinite　patches　and　the　local　approximations　are　designed　to　construct　the　Galerkin　approximation　that　satisfies　the　asymptotic　behavior　of　waves　at　infinite.　Different　from　the　infinite　element　technique　in　the　finite　element　method　(FEM),　where　the　shape　functions　are　required　to　satisfy　not　only　the　continuity　between　finite　and　infinite　elements　but　also　the　attenuation　behavior　of　solution　while　approaching　infinite,　the　NMM　is　demonstrated　more　straightforward　and　elegant　in　the　construction　of　the　Galerkin　approximation.　Some　examples　in　propagation　of　elastic　wave　and　surface　water　wave　are　investigated　to　verify　the　accuracy　and　applicability　of　the　proposed　method.