  This paper is concerned with the theoretical study of plasmonic resonances
for linear elasticity governed by the Lam\'e system in $\mathbb{R}^3$, and
their application for cloaking due to anomalous localized resonances. We derive
a very general and novel class of elastic structures that can induce plasmonic
resonances. It is shown that if either one of the two convexity conditions on
the Lam\'e parameters is broken, then we can construct certain plasmon
structures that induce resonances. This significantly extends the relevant
existing studies in the literature where the violation of both convexity
conditions is required. Indeed, the existing plasmonic structures are a
particular case of the general structures constructed in our study.
Furthermore, we consider the plasmonic resonances within the finite frequency
regime, and rigorously verify the quasi-static approximation for diametrically
small plasmonic inclusions. Finally, as an application of the newly found
structures, we construct a plasmonic device of the core-shell-matrix form that
can induce cloaking due to anomalous localized resonance in the quasi-static
regime, which also includes the existing study as a special case.
