Anisotropic polymer foams have been prepared, which exhibit a Poisson’s ratio exceeding 1, and ratios of longitudinal to transverse stiffness exceeding 50. The foams are as much as 20 times stiffer in the longitudinal direction than the foams from which they were derived. The transformation process involved applying to open-cell polyurethane foam an axial strain of 25 to 45%, at a temperature above the softening point, followed by cooling under axial strain.