Let D1 ⊂ R3 be a non-empty simply connected open bounded set and Γ = ∂D1 be its boundary. We assume Γ to be a C2 surface and let (Γn)n∈N be a sequence of surfaces, such that Γn is closed, , and the surface measure of Γ\Γn is positive for n ∈ N. The set D1 is the cavity associated with (Γn)n∈N. Let HΓn, n ∈ N, HΓ be the self-adjoint operators on L2 associated with the minus Laplace operator with Dirichlet boundary condition on Γn, n ∈ N and on Γ, respectively. Note that, roughly speaking, HΓ is the operator associated with minus the Laplacian on R3\Γ with the Dirichlet boundary condition on Γ. A similar statement holds for HΓn, n ∈ N. We show that the spectral measure, dEΓn (λ), λ ∈ R, associated with the operator HΓn, n ∈ N, when n → +∞ converges to the spectral measure dEΓ (λ), λ ∈ R, associated with the operator HΓ. That is in a sense made precise later we prove that Σ (HΓn) → Σ (HΓ) when n → +∞, where Σ (HΓ) and Σ (HΓn), n ∈ N, are the spectra of HΓ and HΓn, n ∈ N, respectively. Moreover, we show that the point spectrum of HΓ is made of an infinite number of positive eigenvalues of finite multiplicity and that the point spectrum of HΓn, n ∈ N, is empty and that the essential spectrum of HΓn, n ∈ N, and of HΓ is continuous and is contained in [0, +∞). Under the extra hypothesis that Γ is a C4 surface and that the Gaussian curvature of Γ is positive at every point of Γ, we prove that the essential spectrum of HΓ is a continuous spectrum and is given by [0, +∞). So that the convergence of dEΓn (λ), λ ∈ R to dEΓ (λ), λ ∈ R, when n → +∞ can be interpreted as a spectral concentration phenomenon that consists in the fact that the limit of the spectrum of operators with purely continuous spectrum is the spectrum of an operator that is made of eigenvalues embedded in a continuous spectrum.