Patterned silicon on insulator structures representing evenly spaced parallel 15 nm-thick nanostripes exhibit an enhanced Raman scattering response when excited in the visible range in an oblique incidence backscattering configuration. The enhancement phenomenon in two structures having different stripe widths, 200 and 50 nm, is investigated at various sample azimuthal orientations, excitation radiation polarizations as well as laser wavelengths and is shown to be of resonant nature. The enhanced Raman response of the patterned structures is attributed to the presence of Mie resonances, essentially resulting in the enhancement of the internal electric field within the nanostripes. It is quantitatively described in terms of the spheroid particle model extended beyond the electrostatic limit to include field retardation effects that are shown to be responsible for the resonant behaviour in the visible range.