  For the Lam\'{e} operator $\mathcal{L}_{\lambda,\mu}$ with variable
coefficients $\lambda$ and $\mu$ on a smooth compact Riemannian manifold
$(M,g)$ with smooth boundary $\partial M$, we give an explicit expression for
full symbol of the elastic Dirichlet-to-Neumann map $\Lambda_{\lambda,\mu}$. We
show that $\Lambda_{\lambda,\mu}$ uniquely determines partial derivatives of
all orders of the Lam\'{e} coefficients $\lambda$ and $\mu$ on $\partial M$.
Moreover, for a nonempty open subset $\Gamma\subset\partial M$, suppose that
the manifold and the Lam\'{e} coefficients are real analytic up to $\Gamma$, we
prove that $\Lambda_{\lambda,\mu}$ uniquely determines the Lam\'{e}
coefficients on the whole manifold $\bar{M}$.
