Nonmonotonic 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 stabilized from collapse by the volumetric constraint. The objective of this work was to obtain an 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. Commercial polyurethane foams with a pore size of 30 pores per inch (ppi) were subjected to quasi-static volume compression at strain rates of 5 ×10 -3 and slower as well as constant volume bulk relaxation tests at ambient temperature. Negative incremental stiffness was observed in two of three specimens cut from the same parent material, however the detailed behavior was highly specimen and cycle dependent. Time dependent tests disclosed power law behavior for constant volume bulk relaxation. Dynamic tests were affected by parasitic damping in the test apparatus and control electronics. Foams showing negative incremental bulk moduli will be used in future work as inclusions in positive stiffness matrices for the development of exterlibral composites.