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By combining the equation of motion of a magneto-elastically coupled system derived from a classical hamiltonian and the Maxwell equations with the propagation factor neglected, we obtained a differential equation which determines the magnetic oscillations accompanying elastic vibrations of a ferrite specimen of the usual size for magnetic resonance experiments. To each normal mode of elastic vibration of the specimen there exists an associated magnetic oscillation (namely, a magneto-acoustic mode). We pointed out that the magneto-acoustic resonance phenomenon discovered by Spencer and Le Craw is a special case of the parametric oscillation involving a magnetoacoustic and a magnetostatic mode. The arrangements for observing the oscillation involving a certain magnetostatic mode and magnetoacoustic modes and the theoretical estimate of the threshold pumping power were discussed. We derived the equations coupling a magnetoacoustic and a magnetostatic mode under pumping. By analysing the (even or. odd) symmetry of the field quantities involved, we arrived at the selection rules for possible combinations of modes taking part in the parametric oscillations in a small sphere of ferrite. Finally, it was mentioned that attention should, be paid to the parametric amplification of the magnetic field accompanying thermal phonons as a possible source of noise in a ferrite microwave amplifier through the modulation of the pumping power.