The impact dynamics of a flexible multibody system is investigated. By using a partition method, the system is divided into two parts, the local impact region and the region away from the impact. The two parts are connected by specific boundary conditions, and the system after partition is equivalent to the original system. According to the rigid-flexible coupling dynamic theory of multibody system, system’s rigid-flexible coupling dynamic equations without impact are derived. A local impulse method for establishing the initial impact conditions is proposed. It satisfies the compatibility conditions for contact constraints and the actual physical situation of the impact process of flexible bodies. Based on the contact constraint method, system’s impact dynamic equations are derived in a differential-algebraic form. The contact/separation criterion and the algorithm are given. An impact dynamic simulation is given. The results show that system’s dynamic behaviors including the energy, the deformations, the displacements, and the impact force during the impact process change dramatically. The impact makes great effects on the global dynamics of the system during and after impact.