  We prove dispersive estimate for the elastic wave equation by which we extend
the known Strichartz estimates for the classical wave equation to those for the
elastic wave equation. In particular, the endpoint Strichartz estimates are
deduced. For the purpose we diagonalize the symbols of the Lam\'e operator and
its semigroup, which also gives an alternative and simpler proofs of the
previous results on perturbed elastic wave equations. Furthermore, we obtain
uniform Sobolev inequalities for the elastic wave operator.
