It has been observed under certain conditions that a compressible fluid can experience an abrupt change of macroscopic parameters. Examples are detonation waves, explosions, wave systems formed at the nose of projectiles moving with supersonic speeds, etc. In all these cases the wave front is very steep and there is a large pressure rise in traversing the wave, which is called a shock wave.

In the perfect gas approximation shock waves are discontinuity surfaces separating two distinct gas states. In higher order approximations (such as the Navier–Stokes equation) the shock wave is a region where physical quantities change smoothly but rapidly. In this case the shock has a finite thickness, generally of the order of the mean free path.

Since the shock wave is a more or less instantaneous compression of the gas, it cannot be a reversible process. The energy for compressing the gas flowing through the shock wave is derived from the kinetic energy of the bulk flow upstream of the shock wave. It can be shown that a shock wave is not an isentropic phenomenon: the gas experiences an increase in its entropy.

The simplest case for studying shock waves is a normal plane shock wave, when the gas flows parallel to the x axis and all physical quantities depend only on the x coordinate. In this case the normal vector of the shock surface is parallel to the flow direction.