Abstract: The behavior as t→∞ of solutions of the linear system of elastic equations defined on a non-star-tshaped exterior domains in Rⁿ (n ≥ 3) is discussed.It has showed that the local energy decays with arate of t^-1+H (0 ≤ H ≤ 1),nonuniformly with respect to the geometrical properties of the obstacle.and when n is odd the local energy decays exponentially.For the classical elasticwave,when n=3,the behavior of the solution of the nonhomogeneous system with a right side term periodical with respect to time t is discussed.

Key words: Elastic Theory, Asymptotic Behavior Local Energy Decay