  In this paper we study the local behavior of a solution to the Lam\'e system
when the Lam\'e coefficients $\lambda$ and $\mu$ satisfy that $\mu$ is
Lipschitz and $\lambda$ is essentially bounded in dimension $n\ge 2$. One of
the main results is the \emph{local} doubling inequality for the solution of
the Lam\'e system. This is a quantitative estimate of the strong unique
continuation property. Our proof relies on Carleman estimates with carefully
chosen weights. Furthermore, we also prove the \emph{global} doubling
inequality, which is useful in some inverse problems.
