The results are presented for physical modeling, which make it possible to answer a question whether there are any bases for the hypothesis (proposed by M. V. Kurlenya and V. N. Oparin) that at the prefailure stages, the focus zones of rock bursts, earthquakes, and other dynamic events become similar to a peculiar “geomechanical laser system,” i. e., an acoustically active medium capable of coherent seismic-energy radiation. In this context, possible consistency of the acoustic signals formed in structural elements of block media, in terms of both the frequency spectrum and the phase component, is a key issue. In existing approaches to the analysis of the mechanisms of focus zones of dynamic rock-pressure manifestation, as a rule, the fact that quasi-static processes of elastic energy accumulation in the forming focus zones always proceed against an acoustic background (from natural microseisms to complex wave phenomena accompanying pulsed seismic effects from remote earthquakes, explosions, etc.) is ignored. In view of the anomalously low friction in block media (discovered at the Institute of Mining, Siberian Branch, Russian Academy of Sciences), the type of the stress-strain state in geoblocks and the amplitude-period characteristics of the “seismic background” may be decisive in the realization of dynamic event. Therefore, it is natural to ask what happens, for example, to microseisms or acoustic wave packets, that are regular in frequency, in the focus zones of future dynamic events depending on the level of stresses prevailing there. Experimental data are considered for one of the most simple cases where the focus zone is modeled by a set of homogeneous blocks with a stress concentrator in the form of a cylindrical cavity (a “plane” model), while the quasi-static process of external loading is represented by uniaxial compression from a press with weak lateral thrust. The “acoustic background” is specified in a peripheral block of the model in a monochromatic regime. This model relates directly to the acoustic monitoring of the limiting states of rocks around underground workings. It is proved that the prefailure stages of model are characterized not only by convergence of the resonance frequencies in the block system but also by amplification of the harmonic-signal amplitude due to conversion of the stored elastic energy of the structural elements to energy of acoustic signals. The law of exponential decay of harmonic signals from a radiation source is violated here, and the model of the geomaterials becomes an acoustically active medium operating as a peculiar “geomechanical laser system.”