This　paper　presents　a　kind　of　FTWBR　(flexible　two-wheeled　balancing　robot).　Its　main　body　has　a　passive　pitch-joint　which　contains　a　spring　as　elastic　damping.　The　Lagrange　approach　is　used　to　formulate　the　dynamic　model　of　the　robot　moving　in　plane.　Based　on　the　model,　it　is　proved　firstly　that　FTWBR　is　unstable　and　locally　controllable　at　upright　equilibrium　state.　Secondly,　the　impact　of　joint-stiffness　on　the　linear　quadratic　optimal　posture　balancing　control　system　is　analyzed.　The　result　demonstrates　that　the　decrease　of　the　joint-stiffness　will　improve　the　robustness　of　the　control　system　theoretically,　but　it　degrades　the　dynamic　performance　of　the　control　system.　The　proposed　dynamic　model　and　the　analysis　provide　some　theoretical　basis　for　designing　and　controlling　FTWBR.