Purpose. The purpose is to improve, develop and generalize the criterion of a crack initiation taking into account the simultaneous effect of the rock stress state and oscillatory processes. The influence of the oscillation amplitude-frequency characteristics on the critical crack length has to be studied as well. Methodology. The methodological basis of the problem solution is a comprehensive approach that includes the mathematical analysis, numerical methods for solving transcendental equations, analysis of the results in the mathematical package Mathcad. Findings. A crack initiation criterion has been developed considering both static stresses (tensile and compressive) and dynamic stress in an elastic wave spreading in the rock mass. The critical length of the initiated crack is determined depending on oscillation amplitude and frequency, static stress and rock crack resistance. The abrupt change in the critical crack length is defined as an indication of the dynamic rock failure. The values of oscillation frequency provoking a decrease in the critical crack length and dynamic rock failure are determined for different rocks. Originality. New approach is used to describe the rock destruction considering the elastic oscillations in the rock mass. The criterion of a crack initiation has been generalized to consider the action of both tensile and compressive stress near by the crack and harmonic stress in an elastic wave. So, based on a common time-space failure criterion, we take into account the stress which is a sum of quasi-stationary and harmonic components. In this paper we focused on the critical crack length that provokes the crack initiation. The influence of oscillation amplitude and frequency on critical length altering has been estimated for different values of the crack resistance. Practical value. The results obtained in the study of criterion crack initiation, can be used to improve the acoustic forecast of gas-dynamic phenomena by the amplitude-frequency characteristics of oscillations. For this purpose, we defined ranges of harmonic oscillation frequencies in some rocks (fine-grained sandstone, limestone, siltstone, coal) in which the initiating of "short" cracks occurs. And we got the real conditions (for coal), in which a slight change in the oscillation amplitude in the array of rocks leads to a jump in the length of the cracks.

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