A finite element scheme is presented for studying the dynamic response of multi-body systems with components manufactured from orthotropic materials. The formulation presented is exemplified by using fiber-reinforced coraposite laminates. The multi-body system considered in this investigation consists of interconnected rigid and flexible components, each undergoing large angular rotations. The configuration of the elastic components is identified by using two sets of generalized co-ordinates, reference and elastic co-ordinates. Reference co-ordinates describe the location and orientation of a selected body reference while elastic co-ordinates describe the deformation with respect to the body reference. Component modes of elastic components in the system are used to reduce the number of generalized co-ordinates. The system differential equations of motion and the algebraic constraint equations describing mechanical joints in the system are written in terms of mixed sets of reference and modal co-ordinates. Two numerical examples, for a slider crank mechanism and a Peaucellier mechanism, are presented in order to demonstrate the effect of the use of the composites on the dynamic response of multi-body systems. Numerical results showed that the use of composites represents an effective passive control strategy.