Abstract: This invention relates to the oil and gas industry and to exploration and production of water resources, in particularly, for stimulation of fluid flow to the well, e.g., for higher oil production, productivity index, and recovery factor. The disclosed device and method can be used for higher permeability of the pay zone due to creation of a network of microcracks in the bottomhole formation zone and facilitates to increase the flow of oil, or other fluids, from the reservoir to the well. Generation of cyclic pressure pulses with varied amplitude and time parameters and proper localization of pulses in space through mechanism of convective combustion provides a “soft” impact upon the wellbore without risk of damage or formation consolidation; the said impact is achieved by using a device which is a downhole cyclic pressure generator operating by a consecutive combustion of layers of compositions having different combustion rates.