The　numerical　manifold　method　(NMM),　a　Galerkin-type　numerical　method,　has　been　successful　in　the　solution　of　problems　with　finite　definition　domains,　yet　it　has　never　been　applied　to　problems　with　unbounded　domains,　or　exterior　problems.　This　study　aims　to　fill　the　big　gap　by　constructing　infinite　patches,　together　with　the　finite　patches,　to　cover　the　unbounded　domain.　The　local　approximations　of　infinite　patches　can　take　the　asymptotic　estimations　of　the　solutions　at　infinity,　which　are　available　for　all　those　well-established　boundary　value　problems.　Compared　with　the　infinite　element　methods　in　the　finite　element　method　(FEM),　the　construction　of　the　trial　functions　by　NMM　is　more　elegant　in　theory　and　more　systematical　in　methodology,　resulting　in　more　accurate　solutions.　Some　typical　examples　in　potential　and　half-space　elasticity　problems　are　investigated　to　illustrate　the　applicability　and　accuracy　of　the　proposed　method.　(C)　2020　Published　by　Elsevier　B.V.