This paper is concerned with longtime dynamics of semilinear Lamé systems ∂t2u-μΔu-(λ+μ)∇divu+α∂tu+f(u)=b,defined in bounded domains of R3 with Dirichlet boundary condition. Firstly, we establish the existence of finite dimensional global attractors subjected to a critical forcing f(u). Writing λ+ μ as a positive parameter ε, we discuss some physical aspects of the limit case ε→ 0. Then, we show the upper-semicontinuity of attractors with respect to the parameter when ε→ 0. To our best knowledge, the analysis of attractors for dynamics of Lamé systems has not been studied before.