CeO₂ nanopowder samples synthesized by self-propagating room temperature method were investigated by Raman spectroscopy. The phonon modes observed in the low frequency region (ω < 70 cm^-1) can be well described by the elastic continuum model, assuming that nanoparticles are of perfect spherical shape and isotropic. Both rigid boundary and stress-free surface cases were analyzed. The calculated vibrational frequency dependencies on the particle diameter were used to identify the modes: (l =2, n = 0), (l = 0, n = 0) and (l = 0, n = 1). Using the facts that mode frequencies scale inversely with particle dimension (ω ∼ 1/D) and that mode-radiation coupling coefficient for this type of vibrations is 1/ω, the correspondence between the particle size distribution and the Raman intensity was made. Particle diameter values ranging from 7 to 8 nm for the rigid boundary condition give the best description of the experimental spectra. This coincides well with the average particle diameter value of 8 nm acquired from the phonon confinement model.