A nested Chebyshev polynomial surrogate model and an improved particle swarm optimization (IPSO) algorithm are proposed to identify the bounds of input and structural parameters in the inverse dynamical problem of flexible multibody systems with interval uncertainty. Specifically, the dynamical model equations for a multibody system incorporating interval uncertainty are established. The interval midpoint and interval radius are used to describe the given output response with interval uncertainty. The Chebyshev polynomial surrogate model is established for the output response of a flexible multibody system. The IPSO algorithm is used to reverse the interval midpoint and interval radius of the unknown parameters in the flexible multibody system. The Chebyshev polynomial surrogate model is used in the proposed method to approximate the original interval uncertain flexible multibody system, thereby significantly reducing the computational cost of the optimization process of the IPSO algorithm.