We have carried out a theoretical calculation of the differential cross section for the electron Raman scatteringprocess associated with the surface optical phonon modes in a semiconductor quantum disc. Electron states are consid-ered to be confined within a quantum disc with infinite potential barriers. The optical phonon modes we have adoptedare the slab phonon modes by taking into consideration the Frohlich interaction between an electron and a phonon.The selection rules for the Raman process are given. Numerical results and a discussion are also presented for variousradii and thicknesses of the disc, and different incident radiation energies.