  We investigate anomalous localized resonance on the circular coated structure
and cloaking related to it in the context of elasto-static systems. The
structure consists of the circular core with constant Lam\'e parameters and the
circular shell of negative Lam\'e parameters proportional to those of the core.
We show that the eigenvalues of the Neumann-Poincar\'e operator corresponding
to the structure converges to certain non-zero numbers determined by Lam\'e
parameters and derive precise asymptotics of the convergence. We then show with
estimates that cloaking by anomalous localized resonance takes place if and
only if the dipole type source lies inside critical radii determined by the
radii of the core and the shell.
