We　present　an　exact　solution　for　supercritical　configurations　of　axially　moving　beams　with　arbitrary　boundary　conditions.　We　take　into　account　the　geometric　nonlinearity　of　the　traveling　beams　in　supercritical　regime,　and　the　nonlinear　buckling　problem　is　analytically　solved.　A　closed-form　solution　for　the　supercritical　configuration　in　terms　of　the　axial　speed　is　obtained.　Some　typical　boundary　conditions,　such　as　fixed-fixed,　fixed-pinned　and　pinned-pinned,　are　discussed.　More　importantly,　based　on　the　exact　solution,　we　found　a　new　anti-symmetric　configuration　for　the　fixed-fixed　axially　moving　beams.　The　traveling　beam　may　vibrate　around　the　new　anti-symmetric　configuration　at　sufficiently　high　traveling　speeds.　A　good　accuracy　of　the　solution　is　confirmed　by　a　comparison　with　the　data　available　in　the　literature,　and　with　our　own　numerical　results.