Modeling of the global motion of mechanical systems superimposed by large flexible deflections and small deformations are subjects that require special consideration. One of the main problems in the dynamics simulation of moving systems it is the precision of the dynamics equations. Novel generalized Newton – Euler dynamic equations for rigid and flexible bodies are proposed. Unified approach to simulation of rigid and flexible systems is developed. The dynamic equations are expressed with respect to the quasi – velocities and accelerations as for the flexible nodes so for the rigid bodies. The method is independent of the selection of the motion coordinates. The equations are compatible with every program system for Finite Element analysis and applicable as for absolute nodal coordinate formulation so for FE in relative coordinates. The novel methodology and approach to dynamics modeling of rigid and flexible systems considerably improves the precision of the simulation process and the reality of a virtual prototype. The book is devoted to scientists and engineers, as well as, to software developers dealing with the problems of mechanical system simulation, analysis and design.