Summary: We consider a vibrating membrane occupying a domain \(\Omega\) of \(\mathbb R^2\), composed of two materials, with very different densities. These materials fill two domains \(\Omega_1\) and \(\Omega_2\) of \(\mathbb R^2\), and \(\Gamma\) is the interface between them: \(\Gamma = \partial \Omega_1 \cap \partial \Omega_2\).We look at the associated spectral problem. We prove that there are modes which concentrate in a small neighborhood of \(\Gamma\), the whispering gallery modes. We address the cases where \(\Omega_2\), the part with negligible mass, is either a bounded or unbounded domain \((\Omega_2 =\mathbb R^2- \bar {\Omega}_1)\), and the case where \(\Omega_1\) is a concentrated mass: \(\Omega_1= \varepsilon B\), with \(e \to 0\), and the density in \(\Omega_1\) very much higher than elsewhere.