This paper considers the dependence of the sum of the first m eigenvalues of three classical problems from linear elasticity on a physical parameter in the equation. The paper also considers eigenvalues γi​(a) of a clamped plate under compression, depending on a lateral loading parameter a;Λi(a), the Dirichlet eigenvalues of the elliptic system describing linear elasticity depending on a combination a of the Lame constants, and eigenvalues Γi​(a) of a clamped vibrating plate under tension, depending on the ratio a of tension and flexural rigidity. In all three cases a∈[0,∞). The analysis of these eigenvalues and their dependence on a gives rise to some general considerations on singularly perturbed variational problems.This is an article from SIAM Journal on Mathematical Analysis 24 (1993): 327, doi:10.1137/0524022. Posted with permission.</p