This　paper　deals　with　reducing　transverse　vibration　for　an　axially　moving　string　by　a　damped　tensioner.　The　governing　equation　and　the　boundary　conditions　are　derived　for　the　system.　Based　on　the　analysis　of　the　reflection　and　transmission　of　waves　propagating　along　the　string,　the　maximal　energy　dissipation　is　realized　by　determining　the　optimal　damping.　To　simulate　numerically　the　effect　of　vibration　reduction,　the　Crank-Nicolson　scheme　is　applied　to　discretize　the　governing　equation　of　the　string.　The　numerical　results　demonstrate　the　optimality　of　the　determined　damping　in　suppressing　the　transverse　vibration.　Copyright　©　2005　by　ASME.