We theoretically study the phonon modes in the wire-type phononic crystal (WPC) composed of two dissimilar isotropic materials with ”circular” cross sections. The phonon modes are classified into three types, i.e., dilatational, torsional, and flexural modes. We calculate the dispersion relations and corresponding phonon displacement fields for a WPC consisting of InAs and InP and discuss the feature of the phonon modes in this structure.