A series of experiments was carried out with three-layer models constructed of granite chippings, quartz sand, and cement; the inner layer of the models had lower strength. The models were loaded on a servocontrolled press under biaxial compression and supplementary mechanical vibration with 40 and 120-sec periods. The variations in press rigidity allowed both to obtain friable macrodestruction of the inner layer and to conduct the experiment in the post- peak stress state with accumulation of microdestruction. Stress, deformation, and acoustic emission were recorded in the course of the experiment, and ultrasonic sounding was also periodically employed. The main object of research was to find symptoms of transition of the model into the stage of unstable deformation in the absence of the rheological curve. We have established that this transition can be revealed by several indicators, i.e., the appearance of asymmetry in the compression-extension phases of vibration cycles, accumulation of diversity of deformations recorded by spatially distributed sensors, distortion of the waveform during ultrasonic sounding, the growth of the "seasonal" amplitude of the acoustic emission showing an increase in the strain sensitivity of the medium, the appearance of the acoustic silence and subsequent activization. We presume that these symptoms can be used to estimate the onset of the instability stage in the fault zones of the Earth's crust when analyzing the weak seismicity, Earth tides and vibroseis data.