In recent experiments on Gas Dynamic Trap (GDT), as well as in earlier experiments on the GOL-3 device, a new and interesting class of oscillations was observed. Its mode structure and frequency resemble that of a sound wave trapped in the mirror cell as a resonator. Such modes can strongly interact with the bounce motion of ions and thus affect the axial confinement in mirror traps. The modes are probably similar to the global acoustic modes (GAMs) in tokamaks. However, there are significant difficulties in reconciling the existence of such modes with conventional theory of plasma waves. In both GOL-3 and GDT in relevant regimes the electron temperature is far below the theoretical limit for existence (let alone weak Landau damping) of ion-sound waves in homogeneous plasma. We explore different models of inhomogeneous anisotropic non-Maxwellian plasma of a mirror trap in search for possible explanations of the observed phenomena.