Abstract: Flexible multibody systems with light weight and high precision are widely used in practical engineering. The structural parameters (physical parameters and geometric parameters) of the flexible multibody system show randomness due to the existence of many uncertain factors such as actual design tolerance, manufacturing error and environmental temperature. The dynamic model with random structural parameters can objectively reflect the dynamic behavior of the real system, and the influence of the uncertainty of structural parameters on the dynamic response of the spatial flexible multibody system cannot be ignored. A non-intrusive calculation method is proposed based on the generalized-alpha algorithm to study the dynamic response of stochastic spatial flexible multibody system with multiple random parameters. The absolute node coordinate formulation (ANCF) is used to describe the flexible body, and the dynamic model of multibody system is established. The polynomial chaos expansion (PCE) method is used to construct the surrogate model of the stochastic dynamics equation of the system. Then, the stochastic response surface method (SRSM) is embedded into the generalized-alpha method. The regression method of improved sampling (RMIS) and the monomial cubature rules (MCR) are used to determine the sample points respectively. The numerical results are compared with those of Monte Carlo simulation (MCS), and the validity of the proposed algorithm is verified. Under the condition of the same definite integral precision, the calculation results of sample points determined by the monomial cubature rules are more stable and the calculation efficiency is higher.