We have theoretically demonstrated that phonon heat flux can be significantly suppressed in Si and Si/SiO ₂ nanowires with the periodically modulated cross-section area-referred to as the cross-section-modulated nanowires-in comparison with the generic uniform cross-section nanowires. The phonon energy spectra were obtained using the five-parameter Born-von Karman-type model and the face-centered-cubic cell model for description of the lattice dynamics. The thermal flux and thermal conductivity in Si and Si/SiO ₂ cross-section-modulated nanowires were calculated from the Boltzmann transport equation within the relaxation time approximation. Redistribution of the phonon energy spectra in the cross-section-modulated nanowires leads to a strong decrease of the average phonon group velocities and a corresponding suppression of the phonon thermal flux in these nanowires as compared to the generic nanowires. This effect is explained by the exclusion of the phonon modes trapped in cross-section- modulated nanowires segments from the heat flow. As a result, a three- to sevenfold drop of the phonon heat flux in the 50- to 400-K temperature range is predicted for Si and Si/SiO ₂ cross-section-modulated nanowires under consideration. The obtained results indicate that cross-section-modulated nanowires are promising candidates for thermoelectric applications.