A　dynamic　model　for　underactuated　robots　with　link　flexibility　is　presented　using　finite　element　method.　Based　on　this　model,　the　dynamic　coupling　effects　are　analyzed,　including　the　acceleration　coupling　between　active　joints　and　passive　ones,　the　dynamic　coupling　between　passive　joints　and　driving　torques.　A　new　index　is　proposed　to　describe　the　dynamic　coupling　between　the　elastic　deformations　of　flexible　links　and　the　active　as　well　as　the　passive　joints,　respectively.　Comparing　the　simulation　results　of　acceleration　and　torque　coupling　of　underactuated　flexible　system　with　those　of　the　rigid　system,　it　has　been　shown　that　the　former　system　can　obtain　greater　coupling　values　at　the　certain　actuator　configuration.　The　flexible　system　can　supply　a　better　energy　transmission　at　this　configuration.　Therefore,　the　results　indicate　that　the　elastic　deformations　of　flexible　links　have　important　influence　on　the　dynamic　characteristics　of　the　system.　The　dynamic　coupling　effects　are　of　significance　in　structure　design,　configuration　design,　actuator　placement　and　control　of　underactuated　robots　system.