The Poisson's ratios of re-entrant Cu foams with different initial relative densities were studied by resonant ultrasound spectroscopy (RUS). Slight anisotropy in foam was detected by RUS and removed by a small unidirectional compression. The transformation into the re-entrant foam was accomplished by applying a sequence of permanent triaxial compression deformations. The Poisson's ratio first decreases and then increases with increasing compression strain. A minimum in Poisson's ratio of approximately −0.7 for all initial densities was achieved with an appropriate permanent compression strain, compared with −0.6 at similar density determined earlier via optical methods. Foams with higher values of initial density attained minima in Poisson's ratio at lower permanent volumetric compression. The shear modulus increased with increasing volumetric compression ratio, and showed a small hump near the point corresponding to Poisson's ratio minimum.