CaF2 and SrF2 films grown on Si(111) by molecular beam epitaxy were studied by the Brillouin spectoscopy method. The measured velocities of surface acoustic waves are in close agreement with those calculated with a simple model of a layered structure. The only discrepancy was a decrease of the velocity in CaF2 films of about 100 nm thick : this was attributed to the difference of the growth modes at the beginning of CaF2 and SrF2 epitaxy on Si(111).