Fibre network mats composed of stainless steel exhibit an unusually large out-of-plane auxeticity (i.e. high negative Poisson’s ratio ν) when subjected to in-plane tensile loading. In situ observations in a scanning electron microscope suggest that this is attributable to fibre segment straightening. An investigation was carried out on the effects of fibre volume fraction and network thickness on the auxetic response. Weak inter-layer bonding, high fibre content and low network thickness were found to amplify the auxetic effect.