Time-variation　of　meshing　stiffness　is　the　main　internal　excitation　for　the　vibration　and　noise　of　the　gear　transmission　system.　Elastic　deformation　in　the　rolling　contact　process　is　an　important　factor　for　the　meshing　stiffness　variation　of　the　toroidal　drive.　However,　most　of　the　previous　meshing　modeling　of　the　toroidal　drive　is　based　on　the　rigidity　hypothesis.　In　order　to　investigate　the　actual　contact　situation　and　improve　the　stability　of　the　toroidal　drive,　this　paper　focuses　on　the　mathematical　modelling　and　characteristics　analysis　for　the　toroidal　drive　with　elastic　deformation　in　the　conjugating　process　between　the　planet-worm　gear　and　sun-worm　as　well　as　between　the　planet-worm　gear　and　internal　toroidal　gear.　The　elastic　deformation　integrated　coordinate　system　of　the　toroidal　drive　is　introduced.　The　elastic　deformation　velocity　induced　by　contact　force　is　adopted　for　the　first　time　in　the　relative　velocity　of　the　Wills　law　for　the　toroidal　drive.　Then,　based　on　Hertz　contact　theory,　the　relationship　between　elastic　deformation　velocity　and　normal　force　is　studied.　In　addition,　the　influences　of　the　elastic　deformation　on　the　meshing　contact　curve,　helix-lead　angle　and　induced　normal　curvature　are　further　discussed.　©　2013　IEEE.