This chapter includes the main numerical methods commonly utilized in multibody systems, namely those necessary to solve the dynamic equations of motion for constrained multibody systems. In this process, the fundamental aspects associated with the use of direct integration method together with the use of Baumgarte stabilization technique are described. In addition, several numerical algorithms for the integration process of the dynamics equations of motion are presented. An algorithm on contact detection for multibody systems encountering contact-impact events is discussed. Finally, numerical methods to systems of linear and nonlinear equations are analyzed.