For damage evaluation, the stage of superfast catastrophic failure of a medium and its mechanical behavior in a state of self-organized criticality prior to the onset of a blow-up fracture mode is of great interest for identification of its precursors. In this work, the data of experimental and numerical investigations of mechanical behavior of a medium before its catastrophic failure and the onset of a blow-up fracture mode are presented. Rock samples and ceramic specimens are subjected to three-point bending and uniaxial compression testing. Surface velocities of the loaded specimens are registered using a laser Doppler vibrometer. The blow-up regime duration is measured to be about 10-20 ms. The specimens' mechanical behavior is numerically simulated under experimental conditions, including the regime of catastrophic fracture. The model parameters of damage accumulation are determined from a comparison with the experimental data. A number of features of the material mechanical response before the catastrophic fracture are identified, which could be treated as failure precursors.