In this paper are presented theoretical calculations of the linewidth of the Rayleigh phonon propagating along high symmetry directions of the (111) surfrace of Aluminium both for different temperatures and for different values of the phonon momentum. The interatomic potential pf the crystal contains both a harmonic part which describes the normal vibrations of the crystal and a cubic part which is the dominant term of the lifetimes of the vibrations. The calculations show a rapid decay when either the temperature of the momentum transfer decrease, and a large anisotropy with the direction od the momentum transfer.