This paper proposes a novel blast wave mitigation device, consisting of a piston-cylinder assembly. A shock wave is induced inside the device when it is subject to a blast wave. The shock wave propagates inside the device and is reflected repeatedly. The physical processes within the blast wave mitigation device are simulated numerically. Numerical predictions are in excellent agreement with analytical solutions for special cases of the investigated problem that are available in the literature. The peak pressure on the base of the device caused by the blast wave is studied under a number of design parameters. The numerical simulation shows that the pressure of the blast wave can be reduced by over 99%.