In this article, the secular rotational varitation of the Earth whose elastic mantle isdeformed by gravitational attraction of the Moon and the Sun is studied by means ofa Hamiltonian method. The expression of the tidal potential with phase lag is given.The value of the secular deceleration of the Earth's rotation is obtained for the Earthmodel PREM. It theoretically is -5.7×10-22
rad / s2
, which agrees perfectly with thelatost observational results. The results also show that the principle contribution to thisdeceleration is the sectorial tide corresponding to the term m = 2, and that thedeformation produced by the Moon is much more importan than that due to the Sun.