Universal properties of the spectra of certain matrices describing multiple elastic scattering of scalar waves from a collection of randomly distributed point-like objects are discovered. The elements of these matrices are equal to the free-space Green's function calculated for the differences between positions of any pair of scatterers. A striking physical interpretation within Breit-Wigner's model of the single scatterer is elaborated. Proximity resonances and Anderson localization are considered as two illustrative examples.PACS number͑s͒: 03.65.Nk, 41.20.Jb, 72.10.Fk, 72.15.Rn Scattering of scalar waves from various kinds of obstacles is rich of interesting and often unexpected physical phenomena. An example of such phenomenon is the case of fixed frequency sound incident on small identical air bubbles in water ͓1-3͔. Electron or phonon scattering from defects or impurities in crystal lattices give another example. Multiplescattering effects from such objects are nontrivial and require special conditions to manifest themselves in their whole beauty. Already for two scatterers placed together well within the wavelength of the scattered wave field extremely narrow proximity resonances can appear ͓4,5͔. For three scatterers there is the possibility for Efimov's effect ͓6-8͔. For very many scatterers we expect, for some range of parameters, that Anderson's localization can show up ͓9-11͔. It would be nice to have a unified approach encompassing all mentioned effects and giving some more insight into them. We use random Green matrices as a tool to achieve this purpose.The Green's function is one of the fundamental basic building blocks for constructing a self-consistent description of the multiple scattering. In the case of scalar waves the Green's function is something very simple. It describes the spherical outgoing s-wave centered at the scatterers position. In this paper we study the spectra of certain matrices describing multiple scattering of scalar waves from a collection of randomly distributed pointlike objects. The elements of these matrices are equal to the Green's function calculated for the differences between positions of any pair of scatterers. We discover several interesting properties of the spectra of such Green matrices including a striking phase-transition-like behavior when the number of scatterers increases. In the limit of the infinite medium the eigenvalues behave remarkably well in that they distribute themselves not all over the complex plane but only on a fixed line. According to our numerical experience these properties seem not to depend on the specific form of the Green's function used and thus appear to be truly universal.The Breit-Wigner-type model of the single scatterer allows us to give a clear physical interpretation of the obtained results. In this particular case the real and imaginary parts of the eigenvalues of the Green matrix can be considered as first-order approximations to the relative widths and positions of the resonances. Thus it is possible to extract some qualit...