Abstract: 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.