In many industrial applications, complex mechanical systems can often be described by multibody systems (MBS) that interact with electrical, flowing, elastic structures, and other subsystems. Efficient, precise dynamic analysis for such coupled mechanical systems has become a research focus in the field of MBS dynamics. In this paper, a coupled self-propelled artillery system (SPAS) is examined as an example, and the discrete time transfer matrix method of MBS and multirate time integration algorithm are used to study the dynamics and cosimulation of coupled mechanical systems. The global error and computational stability of the proposed method are discussed. Finally, the dynamic simulation of a SPAS is given to validate the method. This method does not need the global dynamic equations and has a low-order system matrix, and, therefore, exhibits high computational efficiency. The proposed method has advantages for dynamic design of complex mechanical systems and can be extended to other coupled systems in a straightforward manner.