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Methane deflagration fracturing is a new reservoir stimulation method that serves the efficient development of shale gas reservoirs. However, the propagation law of deflagration fractures is still unclear. In this paper, a numerical model considering the effect of stress wave impact and gas drive of deflagration fracturing was established based on the continuum–discontinuum element method (CDEM). The correctness of the numerical model was verified by comparing it with a laboratory experiment, the steady and unsteady analytical solutions of gas flow, and the approximate solution of fracture propagation. Then, numerical simulations of methane deflagration fracturing in vertical wells and horizontal wells under different factors were carried out to analyze the fracture mechanism. The results indicate that deflagration fracturing in vertical wells can break through the stress concentration around the borehole; the initial radial fractures are formed under the action of stress wave impact and then propagate substantially under the driving action of high-pressure gas. The in-situ stress difference affects the deflagration fracture propagation and makes the half-fracture length in the direction of maximum principal stress larger than that in the direction of minimum principal stress. The more significant the stress difference is, the more noticeable this deviation will be. When the deflagration peak pressure is high, the reservoir burst degree is large, which is conducive to enlarging the stimulation range of deflagration fracturing. Staged deflagration fracturing in horizontal wells can form 5–8 obvious fractures perpendicular to the horizontal borehole in each explosion section. A large cluster spacing and explosion section length are conducive to expanding the stimulation scope. Moreover, the propagation of deflagration fractures will be induced by the natural fractures, and the natural fracture with a considerable length or a slight angle between the dip angle and the propagation direction of deflagration fractures is more likely to be activated. • The deflagration fracturing for shale gas reservoir stimulation is proposed. • The numerical model considers the effects of stress wave and gas drive. • The propagation law of deflagration fracture is revealed by numerical simulation. • Deflagration fracturing can break the stress concentration to form complex fracture. [ABSTRACT FROM AUTHOR]