  This paper is concerned with longtime dynamics of semilinear Lam\'e systems
$$ \partial^2_t u - \mu \Delta u - (\lambda + \mu) \nabla {\rm div} u + \alpha
\partial_t u + f(u) = 0, $$ defined in bounded domains of $\mathbb{R}^3$ with
Dirichlet boundary condition. Firstly, we establish the existence of finite
dimensional global attractors subjected to critical forcings $f(u)$. Writing
$\lambda + \mu$ as a positive parameter $\varepsilon$, we discuss some physical
aspects of the limit case $\varepsilon \to 0$. Then, we show the
upper-semicontinuity of attractors with respect to the parameter when
$\varepsilon \to 0$. To our best knowledge, the analysis of attractors for
dynamics of Lam\'e systems has not been studied before.
