Leakage　loss　has　great　influence　on　the　performance　of　rotary　positive　displacement　type　expander.　Single　screw　expander　has　very　complex　internal　leakage　law　for　its　sophisticated　three-dimensional　structure.　In　order　to　investigate　the　internal　leakage　law　of　the　expander,　a　mathematical　model　is　built　based　on　the　geometry　structure,　the　influence　of　the　size　of　inlet　port　and　the　diameters　of　the　screw　and　the　star　wheel　on　the　length　of　the　leakage　path　is　analyzed.　Results　shows　that,　during　the　intake　process,　the　length　of　leakage　path　L9　reaches　the　maximum　when　intake　orifice　completely　joined,　the　order　of　leakage　path　length　relationship　in　the　expansion　process　is　L8>L7>L1+L2+L4>L9>L6>L3+L5.　The　length　of　leakage　path　at　the　screw　head　of　the　expander　is　related　to　the　internal　volume　ratio　and　decreases　with　the　increase　of　internal　volume　ratio　during　the　intake　process.　Under　the　condition　of　fixed　internal　volume　ratio,　the　length　of　the　leakage　path　rises　with　the　increased　diameter　of　both　when　the　diameters　of　screw　and　star　wheel　are　equal,　and　the　inlet　port　has　a　far　greater　impact　on　leakage　path　length　which　is　longer　in　the　case　of　different　diameters,　which　provide　basis　data　for　the　analysis　and　calculation　of　the　leakage　rate　in　the　single　screw　expander　and　theoretical　guidance　for　structure　optimization　of　the　expander.　©　2015　Journal　of　Mechanical　Engineering.