We study the extended acoustic-phonon modes in a cylindrical GaAs quantum wire embedded in bulk AlAs. There are two kinds of resonant acoustic-phonon modes related to the wire dimensions: one is entirely extended in the system and the other is almost confined in the wire. Displacement of extended phonon modes in the wire region is enhanced for the resonant modes. The dispersion relations of these resonant modes have subband structures similar to those of confined phonon modes in free-standing wires. Owing to the resonant modes, the extended phonon modes, in the wire region, have characters of confined phonon modes in a free-standing wire rather than the usual bulk phonon modes.