The nature of the frequency spectrum of a Vicsek fractal of any stage has been predicted using an analysis based on local symmetry and self-similarity. The analysis was carried out for transverse vibrations of the fractal with nearest-neighbor interactions. The complete frequency spectrum was found to contain both nondegenerate and degenerate components. The degenerate component of the frequency spectrum of the nth-stage fractal consists of threefold degenerate, D 2 -fold degenerate,..., and D n -fold degenerate modes with D 2 =8 and D n =5D n-1 -8 for n≥3. In particular, D 2 -fold degenerate, D 3 -fold degenerate modes,..., etc., are all persistent modes