The unique properties of nanostructures associated with their low dimensionality give rise to new opportunities for research on efficient thermal-to-electric energy conversion and enhancement of the figure of merit. Efficient engineering of the acoustic phonon energy spectrum is possible in multishell tubular structures produced by a novel high-tech method of self-organization of micro- and nano-architectures [1]. The strain-driven roll-up procedure paved the way for new classes of metamaterials such as single semiconductor radial microand nano-crystals and multi-layer spiral micro- and nano-superlattices. The acoustic phonon dispersion is determined by solving the equations of elastodynamics for InAs/GaAs multishell systems [2]. It is shown that the number of shells is an important control parameter of the phonon dispersion together with the structure dimensions and acoustic impedance mismatch between the superlattice layers. The obtained results suggest that rolled up nano-architectures are promising for thermoelectric applications owing to a possibility of significant reduction of the thermal conductivity without degradation of the electronic transport.