We present a theoretical calculation of the differential cross section for the electron Raman scattering process associated with surface optical phonon modes in semiconductor quantum wires (QWs) with ring geometry. Electron states are considered to be confined within the QWs. We consider the Frohlich electron-phonon interaction in the framework of the dielectric continuum approach. Some singularities for the ring with various sizes in the Raman spectra are found and interpreted. A discussion of the phonon behavior for the QWs with large and small sizes is presented. The numerical results are also compared with those of experiments. (C) 2011 Elsevier B.V. All rights reserved.