Purpose. Deriving the criterion of a crack (joint) initiating under simultaneous effect of the rock stress state and elastic oscillations generated by an external source is the research purpose. Determining the quantitative relations to estimate the contribution of oscillations to crack initiation and creating a theoretical basis for the improvement of rock burst forecasting technique is a goal as well.Methods. The brittle failure theory and a time-space approach are applied to determine a critical length of initiating cracks depending on stress level and amplitude-frequency characteristics of acoustic oscillations. Analysis of experimental data and comparison with the numerical results are carried out. Findings.Quantitative ratios between the critical length of the crack, the stress intensity factor, oscillation amplitude and frequency are determined. It is shown that there are such values of the oscillation frequencies at which the critical crack length is especially sensitive to the amplitude alteration. The increase in the oscillation amplitude initiates starting the crack with small length. Numerical estimation is made for close-grained sandstone using such characteristics as crack resistance factor and Rayleigh' wave velocity and tensile strength. Increasing the amplitude twice at the frequency of 1145 Hz causes the triple reduction of the starting crack length. Numerical results correlate with in situ data related to acoustic predicting the dynamic phenomena in the rock mass.Originality. The crack initiation criterion has been identified. Practical implications.Quantitative relations between stress components and amplitude-frequency characteristics should be used to improve the outburst forecasting technique and increase the reliability of dynamic effect prediction.