An HTS cable assembly is provided which includes a cryostat or housing, an HTS wire bundle disposed longitudinally within the cryostat, and plural support members disposed between the HTS wire bundle and the cryostat. The support members are elongate, tubular members having resiliency in both the axial and radial directions. The support members are disposed between the HTS wire bundle and the inner surface of the cryostat in an arrangement that maintains and supports the HTS wire bundle in a spaced-apart relationship with respect to the inner surface of the cryostat. In addition, the plural support members are configured to substantially prevent relative movement between the HTS wire bundle and the cryostat.