The paper describes the manufacturing and tensile testing of auxetic (negative Poisson's ratio) thermoplastic polyurethane foams, both under constant strain rate and sinusoidal excitation. The foams are produced from conventional flexible polyurethane basis following a manufacturing route developed in previous works. The Poisson's ratio behaviour over tensile strain has been analyzed using an Image Data processing technique based on Edge Detection from digital images recorded during quasi-static tensile test. The samples have been subjected to tensile and compressive tests at quasi-static and constant strain-rate values (up to 12 s-1). Analogous tests have been performed over iso-volumetric foams samples, i.e., foams subjected to the same volumetric compression of the auxetic ones, exhibiting a near zero Poisson's ratio behaviour. The auxetic and non-auxetic foams have been also tested under sinusoidal cycling load up to 10 Hz, with maximum pre-strain applied of 12%. The hysteresis of the cycling loading curve has been measured to determine the damping hysteretic loss factor for the various foams. The measurements indicate that auxetic foams have increased damping loss factor of 20% compared to the conventional foams. The energy dissipation is particularly relevant in the tensile segment of the curve, with effects given by the pre-strain level imposed on the samples.