Non-monotonic load-displacement curves obtained from buckled tubes and single foam cells subjected to displacement controlled uniaxial compression are due to negative stiffness of the structural elements in the post-buckled regime. In the continuum limit, non-monotonic stress-strain curves obtained for elastomeric foams under volume controlled hydrostatic compression indicate negative incremental bulk moduli. Negative bulk moduli arise from cell rib buckling but are stabilized from collapse and shear localization by the volumetric constraint. The objective of this work was to obtain a detailed understanding of the material conditions necessary for non-monotonic constitutive behavior in open celled foam. For instance, amplitude degradation of the previously obtained incremental negative bulk modulus was observed after a small number of cycles. Synthetic and natural (sponge) foams were subjected to dynamic hydrostatic compression to obtain their linear viscoelastic behavior in terms of dynamic modulus and loss tangent in the low frequency regime at ambient temperature. The effects of pore size and pore shape were explored, as well as stability of the foams within the negative incremental bulk modulus region. Foams showing negative incremental bulk moduli will be used as inclusions in positive stiffness matrices for the development of exterlibral composites.