Abstract: For the system of the centre rigid-body mounted on an external cantilever beam,the equilibrium solution of the steadily rotatin g beam is stable if th e effect of its shearing stress(i.e.the beam belongs to the Euler-Bernoulli type)is not considered.But for the deep beam,it is necessary to con sider the effect of the shearing stress(i.e.the beam belongs to the Timoshenko type).In this case,the ten sion buckling of the equilibrium solution of th e steadily rotating beam may occur. In the present work,usin g the general Hamilton Variation Principle,a nonlinear dynamic model of th e rigid-flexible system with a centre rigid-body mounted on an external Timoshenko beam is established.The bifurcation regular of the steadily rotatin g Timoshenko beam is investigated by using numerical methods.Furthermore, the critical rotating velocity is also obtained.