The hydrostatic compaction of composites comprising a closely-packed particle-bed filled by a dense matrix is measured experimentally using a fluid-pressurization apparatus. A highly compliant polymer or pure aluminium are infiltrated into preforms of packed alumina particles containing between approximate to 56 and approximate to 63 vol pct reinforcement. With the compliant matrix data show a non-linear response. This is rationalized using a simple model of compressive granular media elasticity based on the Hertz-Mindlin model. Bulk moduli for the aluminium matrix composites are found to be relatively constant; comparison with theory shows that, unlike what is observed for deformation involving shear, in hydrostatic elastic compression the classical self-consistent model describes best measured modulus values for this class of composite.