The elastic properties of thermoplastic elastomers based on poly(tetramethylene oxide) and monodisperse amide hard segments (HS) were studied in compression and tensile mode as well as with stress relaxation (SR) measurements. For these copolymers the compression set values were low and increased with the modulus and temperature. At low strains (< 50%) the tensile set (TS) values were low and the strain recovered almost completely with time. Furthermore, the TS values increased with strain, due to a deformation of the crystallites and a strain hardening of the polyether segments. During the SR measurements, two processes were observed: a fast initial decay in the first 10 s followed by a relaxation process that was dependant on the logarithm of time. The initial decay during the first seconds increased with the modulus of the copolymers and with the applied strain. The SR values for the second process, normalised to the stress at 100 s, were independent of the strain (within the range of 25-300%) and only little dependant on the modulus of the system. In comparison to the literature data the copolymers with the monodisperse HS displayed improved elastic properties and low SR values.