To account for the nonlinear dynamic effects of flexible sandwich plates undergoing large deformation, a computational method for dynamic analysis of flexible sandwich plates is studied. According to the characteristics of sandwich plates, a simplified plate model is proposed based on the Kirchhoff plate theory, in which the shear stiffness of the core plate is neglected and the stiffness for the whole plate is derived. For the dynamic problem of flexible multibody systems, a thin plate element has been studied based on the absolute nodal coordinate formulation (ANCF). Meanwhile, a method based on invariant tensors is proposed for calculating elastic forces and their Jacobians, which can be calculated during preprocessing and applied for programmed calculation. Using examples, the proposed computational method is verified to be feasible and accurate. In addition, a benchmark example and a double-pendulum model are used to verify the applicability and feasibility of our analytical method for flexible sandwich plates in flexible multibody systems. Therefore, this method lays a foundation for the study of flexible dynamics problems regarding multibody systems with sandwich plates.