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Using a Green function method based on an atomic vibration model, herein we report the results from our investigation of phonon transport through multiple Si/PtSi layered structures. In contrast with values predicted using elastic wave theory and an impedance mismatch method, we find that a detailed atomic-vibration approach exhibits significantly suppressed phonon transport and leads to a 30-times reduction of the thermal conductance, compared to that of Si bulk. We attribute the origin of the suppression to the lack of PtSi phonon modes in the energy range of 20-30 meV, and to the effects of interface scattering between Si and PtSi layers. [ABSTRACT FROM AUTHOR]