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In this paper, we theoretically describe a magnetoelastic system with an explosive instability in which the magnetic energy can be converted into the mechanical one via an extremely efficient channel. The principle is based on the amplification of acoustic waves traveling in an antiferromagnetic crystal under the action of transversal electromagnetic pumping. It is known that such parametric interaction can produce an exponential acoustic wave amplification. Our finding consists in the addition of another pumping channel by means of a discrete resonant acoustic mode whose impact is similar to the Feshbach resonance observed in another physical system (ultra-cold gazes). The addition of the second pumping mechanism results in the explosive instability having the dynamics of a singularity at a finite time instead of the exponential growth. In our example the traveling waves are Lamb waves in an antiferromagnetic plate, and the additional pumping is a shear resonance. We establish equations governing the considered three-phonon parametric instability, theoretically analyze the instability conditions, and give a relevant numerical example illustrating the explosive magneto-acoustic dynamics. It is shown that the explosive scenario can occur with a very low signal level i.e. Lamb waves amplitudes comparable to spontaneous noise in the system.