This work is an experimental and theoretical study of vibration in the gas medium of a vessel containing a fluid with the free surface. The phenomenon of fluid aeration in this case is observed at sufficiently low frequencies and is caused by the free surface discontinuity (i.e. ruptures of the surface layer). This is theoretically confirmed by origination of a parametric instability of the free surface at frequencies close to those observed at the experiments. The non-linear differential equation of gas bubble motions in the gas-fluid medium and rather simple conditions of dipping bubbles are derived on the basis of the vibrational mechanics approach and the method of direct separation of motions. The continuum model describing the formation of a layer saturated with gas bubbles near the free surface and its further evolution in the vibrating vessel is also suggested. The obtained model is consistent with the model based on the vibrational mechanics approach.