The problem of the reflection of a shock wave from a moving boundary is examined in an idealized one‐dimensional treatment. We consider in detail the head‐on collision of an incident step shock wave and a piston moving at constant velocity into a gas at rest. The calculation involves the head‐on collision of two shock waves and the subsequent reflection of an altered transmitted wave from the piston. The reflected pressure is calculated for a range of incident shock strengths and piston speeds. For a stationary piston both the absolute and excess reflected pressures are at most eight times the absolute or excess pressure of the incident shock wave (with &ggr;=7/5). With a moving piston, however, this limiting factor is greater than eight, but finite for finite piston speed and infinite incident shock strength, and is infinite for infinite piston speed and finite incident shock strength. This last result holds even in the limit of the incident wave being an acoustic pulse. The method of solution for shock‐wave interaction with a piston receding at constant velocity is also indicated. Although the shock is strengthened on passing through the piston rarefaction wave, the reflected overpressure is less than that resulting from the same initial shock wave reflecting from a stationary piston.