The authors study electron-SO-phonon coupling in the case of Frohlich interaction in cylindrical quantum wires. The polaron self-energy and renormalized effective mass due to surface optical phonons in cylindrical quantum wires have been calculated as functions of the radius of the wire by the standard LLP intermediate-coupling method. It is found that the strength of electron-SO-phonon coupling is strongly dependent on not only the size of the wires but also the dielectric constant of the surrounding medium. The authors numerical results show that the effects of surface optical phonons are very significant and cannot be neglected in thin wires.