In order to avoid the global dynamics equations and increase the computational efficiency for multibody system dynamics (MSD), the transfer matrix method of multibody system (MSTMM) has been developed and applied very widely in research and engineering. It differs from ordinary methods in multibody system dynamics with respect to the features that there is no need for a global dynamics equation, and it uses low‐order matrices for high computational efficiency. For linear multibody systems, the solution of MSTMM is exact even if continuous elements like beams are involved. The discrete time MSTMM, however, has to use local linearization. In order to release the method from such approximations, a novel version of MSTMM is developed where translational and angular accelerations, on the one hand, and internal forces and moments, on the other hand, are used as state variables. Already linear relationships among these quantities are utilized, which results in new element transfer matrices and algorithms making the study of multibody systems as simple as the study of single bodies. This approach also allows combining MSTMM with any general numerical integration procedure. Two chapters are provided in this part: the transfer matrix method for multi‐rigid‐body systems is introduced in Chapter 5 and the transfer matrix method for multi‐flexible‐body systems is presented in Chapter 6.