We discuss here the use of a mechanical suspension for the new generation of resonant gravitational wave antennas, cooled at temperatures below 0.1 K. The crucial problem of these detectors is the isolation from all external mechanical vibrations in the presence of the unavoidable solid thermal link with a dilution refrigerator. Measurements of the mechanical transfer function performed with two types of suspension‐thermal link configurations are reported. This study has led to the design of the suspension and thermal link of the first ultralow temperature antenna of the Rome group ‘‘Nautilus.’’