Blast protection using cellular materials is being actively pursued at research and technology levels. The present work uniquely demonstrates the generation of stress waves, strain waves and mass velocities in monolithic closed cell aluminium foams of different densities and lengths subjected to simulated blast loads and their combined effect on blast attenuation. The foams were assumed to be resting against a rigid end wall. If the numerically calculated stress at the back face was less than the applied stress at the front face, the interaction was termed blast mitigation or attenuation. The results show that ‘pressure mitigation’ occurs for low-density foams whose plastic strength is less than the applied pressure, but pressure amplification for high-density foams whose plastic strength is higher than the applied pressure. The pressure amplification observed in shorter length high density foams transformed to pressure mitigation if the foams were sufficiently long. Based on these results and other stress, strain and velocity related diagnostics, the underlying mechanism behind blast wave amplification/mitigation and its relation with foam density and length is proposed.