A self‐consistent multiple scattering approach with suitable pair‐correlation function has been employed to study the frequency‐dependent properties of rubber materials containing a random distribution of voids. Numerical results indicate that for a certain range of concentration of voids, the resonance of the voids controls the frequency‐dependent effective properties such that the imaginary part of the effective wavenumber becomes greater than the real part. This indicates that the propagating wave will be damped out over a distance smaller than a wavelength. The so‐called ‘‘superviscous’’ propagation seems to occur over a bandwidth controlled by the concentration of voids (c). The bandwidth increases with increasing concentrations in the range 0