Summary: We consider a problem in three-dimensional linearized elasticity, posed over a domain consisting of a plate of thickness \(2\epsilon\), inserted into a three-dimensional supporting elastic structure. Assuming that the Lamé constants of the material constituting the plate vary as \(\epsilon^{-3}\) and that those of the supporting structure vary as \(\epsilon^{-2-s}\), \(s>0\), we establish the \(H^ 1\)-convergence of the (appropriately scaled) components of the displacement vector field, as \(\epsilon\) approaches zero, towards the solution of the well-known boundary value problem of a clamped plate. In this fashion, we show that the classical boundary conditions of a clamped plate can be obtained by a rigorous “limit analysis” that also takes into account the elastic character of the supporting structure.