The　hysteresis　phenomenon　frequently　arises　in　two-dimensional　(2D)　material　nanoindentation,　which　is　generally　expected　to　be　excluded　from　characterizing　the　elastic　properties　due　to　the　imperfect　elastic　behaviour.　However,　the　underlying　mechanism　of　hysteresis　and　its　effect　on　the　characterization　of　the　mechanical　properties　of　2D　materials　remain　unclear.　Cyclic　loadings　are　exerted　on　the　suspended　monolayer　molybdenum-disulfide　(MoS2)　films　in　atomic　force　microscopy　(AFM)　nanoindentation　experiments.　The　elastic　hysteresis　loops　are　observed　for　most　of　the　force-displacement　curves.　The　friction/wear　between　the　AFM　silicon　tip　and　the　MoS2　monolayer　is　deemed　to　be　dominant　compared　to　the　friction　between　the　monolayer　and　the　silicon　dioxide　substrate　after　the　analysis,　as　determined　using　the　finite　element　method　(FEM)　simulation.　The　loading　force-displacement　curves　instead　of　the　unloading　curves　have　been　used　to　deduce　the　elastic　mechanical　properties　using　a　modified　regression　equation.　The　mean　value　of　the　obtained　Young＇s　modulus　of　monolayer　MoS2,　E,　is　equal　to　209　+/-　18　GPa,　which　is　close　to　the　inherent　stiffness　value,　predicted　by　first　principles　calculation.　Our　results　have　confirmed　that　it　is　not　obligatory　to　exclude　the　sample　data　with　hysteresis　behaviour　for　characterizing　the　elastic　properties　of　2D　materials.　In　addition,　all　sample　sheets　have　finally　been　penetrated　and　the　mean　breaking　stress　value,　sigma(max),　is　36.6　+/-　0.9　GPa,　determined　using　the　radius　value　of　the　worn　tip.　Furthermore,　the　effect　of　the　loading　force　and　the　shape/size　of　the　suspended　monolayer　MoS2　sheets　on　the　hysteresis　behaviour　in　the　2D　nanoindentation　have　also　been　analyzed　and　discussed,　exhibiting　interesting　trends.　Our　findings　provide　guidance　for　the　characterization　of　the　mechanical　properties　of　2D　materials　using　the　AFM　nanoindentation　and　the　experimental　samples　with　elastic　hysteresis　behaviour.