  Transient Elastography enables detection and characterization of tissue
abnormalities. In this paper we assume that the displacements are modeled by
linear isotropic elasticity system and the tissue displacement has been
obtained by the first step in hybrid methods. Then we reconstruct the Lam\'e
parameters of this system from knowledge of tissue displacement. We show that
for a sufficiently large number of solutions of the elasticity system and for
an open set of the well-chosen boundary conditions, $(\lambda,\mu)$ can be
uniquely and stably reconstructed. The set of well-chosen boundary conditions
is characterized in terms of appropriate complex geometrical optics solutions.
