This　paper　focuses　on　deriving　the　dynamic　model　of　a　novel　flexible　mobile　robot,　which　has　elastic　joint,　so　that　the　robot　is　able　to　be　simulated　with　a　computer　and　analyzed　dynamically.　First,　the　dynamic　equations　are　derived　from　Routh　formulation　with　the　nonholonomic　constraints　of　the　robot,　and　then　the　nonholonomic　constraint　forces　are　removed　so　that　the　dynamic　equations　are　transformed　to　an　input-affine　form　at　last.　Three　illustrative　simulation　results　are　given　which　show　that　the　dynamic　model　presented　in　this　paper　is　reasonable.