ThisinvestigationpresentstheGreenfunctionsforadecagonalquasicrystallinematerialwithaparabolicboundarysubjecttoalineforceandalinedislocationbymeansofthecomplexvariablemethod.ThesurfaceGreenfunctionsaretreatedasaspecialcase,andtheexplicitexpressionsofdisplacementsandhoopstressattheparabolicboundaryarealsogiven.Finally,thestressesanddisplacementsinducedbyaphononlineforceactingattheoriginofthelowerhalf-spacearepresented.