Dynamic compaction in foams produced by a finite disturbance, which is associated with the propagation of a compaction front, is investigated. The compaction front resembles a shock front with a jump in the field variables across the front. The dynamic compaction of foam produced by a blast pressure wave is investigated using a numerical analysis approach, which considers fluid-structure interaction (FSI) within an Arbitrary-Euler Lagrange (ALE) framework. It is shown that during dynamic compaction, the total energy dissipated in the irreversible compaction, which can be assessed as the difference between the work done by the blast pressure wave and the kinetic energy of the compacted foam, is significantly higher than the value obtained by considering a loading path given by the static stress-strain response of the material.