Abstract: Firstly,the stochastic nonlinear dynamic model of the multi-body mechanical system was established, the Itô differentiation equation and the corresponding FPK equation of the response-transition probability density function with the diffusing process were obtained.Then,the Hopf bifurcation behavior of the planar multi-body mechanical system was studied by using the quasi-nonintegrable Hamilton system theory.The conditions of local and global stability of the system were discussed by largest Lyapunov exponent and boundary category.Finally,the functional image of stationary probability density and jointly stationary probability density were simulated to verify the theorectical results.