Abstract: In order to solve the problems of high break-down pressure, single fracture shape and unsatisfactory stimulation effect in the conventional fracturing process, many new fracturing technologies change the steady-state liquid injection mode, and improve the fracturing effect by using the dynamic effect generated by unstable excitation.However, most of the current researches on the stress distribution, initiation and propagation of hydraulic fractures are based on static assumptions.In view of the above problems, an elastic dynamics model of the reservoir rock under the excitation of unstable wellbore internal pressure is established, and the perfectly matched layer method is used to simulate the infinite reservoir at the outer boundary of the model.The dynamic model is solved by finite difference method and finite element method respectively.Furthermore, the dynamic stress distribution in the reservoir is analyzed.Also, the circumferential stress response amplitudes under different excitation frequencies and the dynamic characteristics of different lithologic reservoirs are compared and studied.The results show that the calculation results of the two numerical simulation methods are basically consistent.The circumferential stress produced by in-situ stress near the wellbore is negative, showing compression.Before hy-draulic fractures initiation, the internal pressure of the wellbore must first overcome the influence of in-situ stress, and the circumferential stress of the wellbore inner wall takes the maximum value in the direction perpendicular to the minimum horizontal principal stress of the reservoir.Due to the high natural frequency of reservoir rock, increasing the excitation frequency in the low frequency range(< 100 Hz) has little effect on the amplitude of dynamic stress fluctuation in the reservoir.To further improve the fracturing effect, the excitation frequency should be designed according to the dynamic characteristics of different lithologic reservoirs as far as possible under the constrains of technologies and costs.The resonance frequency of coal is smaller than that of sandstone, in other words, a better fracturing effect can be achieved under a lower excitation frequency.The research results can pro-vide a theoretical guidance for the calculation of break-down pressure of reservoir rock under unstable excitation and the selection of excitation frequency in fracturing design.