Abstract: Based on the impact/rub dynamic equation for Jeffcott rotor in a rotary machine with mass eccentricity, the stochastic response to the impact/rub acted on a rotor-stator box system is systematically investigated by way of Kronecker algebra, matrix calculus, second order moment analysis of vector-valued and matrix-valued functions, matrix perturbation theories and probability statistics methods. The generalized mathematical expressions of both first order and second order moments in the stochastic response are thus derived with numerical solutions given. Analyzes the stochastic responses to the random parameters of the rotor-stator box system, such as the shaft stiffness and damping, stator stiffness and damping, eccentricity and radial stiffness of stator. The results indicate that in the rotor system a strong vibration takes place initially, to which the response amplitude is greater than the radial clearance between rotor and stator, thus leading to impact/rub.