This book analyzes several compliant contact force models within the context of multibody dynamics, while also revisiting the main issues associated with fundamental contact mechanics. In particular, it presents various contact force models, from linear to nonlinear, from purely elastic to dissipative, and describes their parameters. Addressing the different numerical methods and algorithms for contact problems in multibody systems, the book describes the gross motion of multibody systems by using a two-dimensional formulation based on the absolute coordinates and employs different contact models to represent contact-impact events. Results for selected planar multibody mechanical systems are presented and utilized to discuss the main assumptions and procedures adopted