In this chapter, we shall be concerned with the class of problems in which the plastic deformation is so rapid that the inertia effects cannot be disregarded. Problems of dynamic plasticity arise in the high-velocity forming of metals, penetration of high-speed projectiles into fixed targets, enlargement of cavities by underground explosion, and design of crash barriers related to collisions, to name only a few. The rate of loading and the size of the components are usually such that the deformation process can be described in terms of the propagation of elastic/plastic waves. However, simplified theories which disregard the wave propagation phenomenon are generally capable of providing useful information for practical purposes. In the case of structural members subjected to impact loading, the mode of plastic deformation can be most conveniently represented by the existence of discrete yield hinges that rapidly move away from the point of loading. The concept of moving yield hinges is a useful device for the dynamic analysis of structures.