This　article　investigates　the　stabilization　problem　of　stop-and-go　waves　in　vehicle　traffic　flow　with　bilateral　boundary　feedback　control.　The　stop-and-go　waves　induce　the　discontinuities　of　vehicle　speed　and　density,　which　inturn　lead　to　different　traffic　states　on　the　front　and　back　sides　of　the　shock　front.　According　to　the　Rankine-Hugoniot　condition,　a　propagation　equation　of　the　shock　front　is　proposed　depending　on　the　characteristic　velocities　of　the　Aw-Rascle-Zhang　traffic　flow　model.　Then,　the　complete　dynamics　of　the　stop-and-go　waves　is　formulated　as　a　coupled　hyperbolic　partial　differential　equations　(PDE-　PDE)　system　with　a　common　moving　boundary.　The　well　posedness　of　the　coupled　system　with　the　moving　boundary　is　established　via　the　fixed-domain　method.　To　stabilize　the　discontinuous　traffic　state　and　the　location　of　shock　front　simultaneously,　the　bilateral　boundary　feedback　control　is　formulated　for　the　stop-and-go　waves　of　traffic　flow.　Some　sufficient　conditions　in　terms　of　matrix　inequalities　are　derived　for　ensuring　the　local　exponential　stability　of　the　closed-loop　system　in　the　H-2-norm.　Finally,　the　theoretical　results　are　illustrated　with　numerical　simulations.