The chapter focuses on dynamics modelling and touches also design aspects of elastic robots. This chapter assumes the reader to be familiar with the basics of kinematics, dynamics, and control of ideally rigid robots. It aims to equip the reader with knowledge and tools to analyse and quantify the various desired and undesired effects of elasticity on the robot operation. Furthermore, the chapter provides techniques for dealing with undesired elasticity and criteria to intentionally synthesise elastic structural members. In its eight sections, the chapter introduces into general terminology, mathematics and dynamics of elastic multi-body systems. It covers elastic joints and transmissions as well as robots with elastic links. Advanced topics guiding the reader to current and emerging fields of research include considerations and criteria for intentional elastic robot design as well as variable impedance actuation.