This book presents a method and a toolbox of Matlab & Simulink programs that are used to generate the dynamic model of a multi-body system for space applications. Two comprehensive examples of multi-body spacecraft along with their Matlab files are presented in this book. The multi-body system that is treated by this method, is composed of a main body (hub) with rigid and flexible bodies attached to it, such as solar panels, antennas, propellant tanks, ..etc. The appendages can be connected to the hub by cantilever or pivot joints. In addition to that, the appendages can have an infinite number of flexible sub-attachments to them in an open mechanical chain. In this method, the rigid six degrees of freedom (three translational and three rotational) can be treated altogether. Every added pivot joint adds a degree of freedom to the system. The Matlab toolbox presented here, was completed as a masters project in Dr. D. Alazard's research labs in École Nationale Supérieure de l'Aéronautique et de l'Espace-Toulouse, France, for the purpose of aiding in the design of spacecraft Attitude and Orbit Control Systems (AOCS).