In the previous chapter, a series of examples was given to illustrate a range of material responses that stem from impact or explosion and result from a transient loading pulse within the material. These drivers propel waves travelling through solids, liquids and gases and place the material they have swept through into a state of compression, tension or shear. This chapter will describe these disturbances in more detail and attempt to give simple mathematical descriptions of the phenomena and the material's response. This basic approach is really a development of solid (a branch of continuum) mechanics to embrace additional features of loading at higher speeds and amplitudes; there are many, more complete texts available on the basics of solid mechanics that the reader may consult. The strategy here is to keep the derivations as simple as possible; again there are texts that derive relations with more generality than here but it is vital that the reader realises the assumptions, and more importantly their limits, in what follows. Particularly, it should be noted that solid mechanics assumes material behaviour based upon observations made in ambient states. Electronic bonding itself changes nature at around 300 GPa, so it is unrealistic to expect theory extended from the elastic state to apply in these regimes. Thus assumptions made and their limitations in the loading states the reader wishes to consider must be fully understood before using the formulae below. The basic laws of conservation of mass, momentum and energy, and classical mechanics will drive the descriptions of the thermodynamic states. To that will be added the concepts of elastic and inelastic (in metals, plastic) deformation bounded by a yield surface. To focus on material response, it is generally the simplest loading that is applied experimentally. Thus these states will be mentioned below to highlight particular relations to which the text will return.