A numerical model for the simulation of the interaction of weak shock waves with open-cell compressible porous foams is developed. It is assumed that the foam is infinitely weak and that its volume fraction, which was 0.05 in the cases studied herein, is relevant only when the interaction between the gaseous and the solid phases is considered. The gas is assumed to be inviscid and thermally nonconductive, except for the viscous drag interaction and the heat transfer between the two phases. It is also assumed that the heat transfer between the two phases is extremely efficient, i.e. that the heat transfer coefficient is infinitely large. The range of incident shock wave Mach numbers investigated herein is between 1.08 and 1.40, and the range of foam densities is between 14.8 and 57.4 kg/m3. The numerical results are in very good agreement with experimentally obtained pressure histories and foam particle paths when the incident shock wave Mach numbers are between 1.25 and 1.40 (weak shocks). The agreement between experimentally and numerically obtained pressure histories is poor when the incident shock wave Mach numbers are between 1.08 and 1.18 (very weak shocks). The results of the study indicate that when weak shocks interact with open-cell compressible foam, the transfer of momentum between the gaseous and the solid phases is of paramount importance. On the other hand, if the shocks are very weak, then the elasticity of the foam is an important parameter as well. It is therefore suggested that, while yielding very good results for weak shocks, the assumption of infinitely weak foam is inadequate for very weak shocks.