This chapter discusses the modeling techniques for mechanical systems in either translational or rotational motion, or both. We begin this chapter with an introduction of mechanical elements, including mass elements, spring elements, and damper elements. The concept of equivalence is discussed, which simplifies the modeling of systems in many applications. We then review Newton’s second law and apply it to translational systems. For rotational systems, moment equations are used to obtain dynamic models. For systems involving both translational and rotational motions, equations of motion can be derived using the force/moment approach, based on Newtonian mechanics, or the energy method, based on analytical mechanics. Examples are given to illustrate both methods, followed by a brief coverage of gear–train systems. The chapter concludes with simulation of mechanical systems, using MATLAB®, Simulink®, and SimscapeTM computer tools.