The　finite　element　theory　is　employed　to　investigate　the　theory　and　method　for　dynamics　modeling　of　planar　parallel　manipulators　with　flexible　links.　The　elastic　displacements　of　the　sub-chains　and　the　relation　between　elastic　displacements　are　analyzed.　The　kinematic　constrain　conditions　and　dynamic　constrain　conditions　of　the　flexible　parallel　manipulators　are　proposed.　Considering　the　effects　of　distributed　mass,　lumped　mass,　shearing　deformation,　bending　deformation,　tensile　deformation　and　lateral　displacements,　the　kineto-elastodynamics　theory　and　Lagrange　formulation　are　employed　to　derive　the　dynamic　equations　of　planar　flexible　parallel　manipulators.　The　elastic　vibration　characteristics　of　the　flexible　planar　parallel　manipulator　are　well　illustrated　through　the　numerical　simulation　of　a　planar　3-RRR　parallel　manipulator.　The　flexibility　of　links　is　demonstrated　to　have　significant　impact　on　position　error　and　orientation　error　of　the　moving　platform.