Geosynthetics　could　reinforce　embankment　subjected　to　localised　sinkholes　to　prevent　embankment　from　collapsing　suddenly　and　decrease　free　surface　settlements.　With　the　trapdoor　experiment　statistics,　a　simplified　Terzaghi＇s　formula　was　proposed　to　calculate　the　vertical　loads　on　the　geosynthetics　over　localised　sinkholes.　Analytical　solutions　to　the　vertical　displacement　of　the　geosynthetics　spanning　localised　sinkholes,　the　tension　force　in　the　geosynthetics　and　the　free　surface　settlements　above　sinkholes　were　deduced　under　the　assumption　that　there　was　an　inverse　triangular　load　distribution　perpendicular　to　geosynthetics　bridging　relatively　small　sinkholes.　A　new　method　was　presented　to　design　geosynthetic-reinforced　embankments　over　localised　sinkholes　considering　the　serviceability　limit　state　and　the　ultimate　limit　state　simultaneously.　The　influences　of　the　parameters　including　the　size　of　sinkholes,　embankment　height,　internal　friction　of　embankment　soil　layers,　etc.　on　free　surface　settlements　and　the　maximum　tensions　of　geosynthetics　were　investigated.　The　results　indicate　that　the　size　of　the　sinkhole　is　the　most　important　factor　in　selecting　the　geosynthetic　reinforcement.　Besides,　the　free　surface　settlement　cannot　be　reduced　significantly　by　enhancing　the　geosynthetic　stiffness　as　the　geosynthetic　stiffness　has　increased　to　a　certain　extent.　©　2018,　Central　South　University　Press.　All　right　reserved.