Unsteady (or “surge”) conditions occur when the flow is accelerating or decelerating, as happens when valves are closed or turbines shut down. Such conditions often continue for only a very short period, but nevertheless, the effects on the system may, under some circumstances, be dramatic (including pipe bursts). In this chapter, the meaning of pressure surge in pipelines, the difference between incompressible and compressible surge and the meaning of the term “shock wave” are explained. Equations are developed to calculate the surge pressure in a simple rigid – or elastic – walled pipe for complete shutdown, and the implications of instantaneous, rapid and slow shutdown are detailed. Worked examples and problems for solution are also given in the text.