In　view　of　the　fact　that　the　flexible-links　parallel　robot　is　an　extremely　difficult,　nonlinear,　strong-coupling　complicate　system　which　has　a　bad　control　property,　an　investigation　was　made　on　resisting　robot　elastic　vibration　caused　by　structural　flexibility　and　high　speed　motion.　On　the　basis　of　Kineto-elastodynamics(KED)　theory　and　finite　element　method,　the　governing　equations　of　high-speed　flexible　parallel　robot　were　developed.　The　elastodynamic　response　of　the　flexible　parallel　robot　was　calculated.　By　applying　the　input　motion　programming　method　which　will　facilitate　the　design　and　realization,　an　effective　method　was　obtained　for　inhibiting　vibration,　with　which　the　effect　of　structural　flexibility　on　position　precision　can　be　remarkably　reduced.　The　proper　input　motion　parameters　was　investigated　to　efficiently　suppress　the　elastic　vibration.　With　the　control　scheme,　the　elastic　vibration　control　of　a　planar　3-RRR　parallel　robot　with　flexible　links　and　rigid　moving　platform　was　utilized　as　an　illustrative　example.　The　proper　input　motions　were　exerted　to　reduce　the　elastic　vibration.　The　simulation　results　show　that　the　elastic　vibrations　have　been　greatly　suppressed.　The　simulation　indicates　that　the　control　method　based　on　the　input　motion　programming　method　is　feasible　and　effective　for　reducing　the　elastic　vibration　amplitude　of　flexible　parallel　robots.