We have theoretically investigated the effect of a coating made of the elastically dissimilar material on the acoustic phonon properties of semiconductor nanowires. It is shown that the acoustic impedance mismatch at the interface between the nanowire and the barrier coating affects dramatically the phonon spectra and group velocities in the nanowires. Coatings made of materials with a small sound velocity lead to compression of the phonon energy spectrum and strong reduction of the phonon group velocities. The coatings made of materials with a high sound velocity have opposite effect. Our calculations reveal substantial re-distribution of the elastic deformations in coated nanowires, which results in modification of the phonon transport properties, and corresponding changes in thermal and electrical conduction. We argue that tuning of the coated nanowire material parameters and the barrier layer thickness can be used for engineering the transport properties in such nanostructures.