Abstract: Coal bump is a stress sensitive dynamic disaster. It is of great significance for scientific evaluation and prevention of coal bump to quantitatively describe the spatial characteristics of stress flow in coal and rock medium.Therefore, the idea of coal bump stress flow theory was improved in this paper, and the idea that stress flow represents the stress rate in time and stress gradient in space was pointed out. The concepts of stress flow tensor and stress flow vector were proposed. It was pointed out that the stress flow tensor describes the flow trend of stress in different locations at different times, and the stress flow vector is always in the same direction as the stress gradient increment. Theoretical derivation shows that the stress intensity factor increases with the stress flow, which could lead to the material failure. The stress flow calculation program was developed using nonlinear finite element method to realize the visualization of stress flow. The dynamic stress states under uniaxial compression test and single coal seam under pillar mining conditions were simulated by the finite element program. The results show that the stress flow vectors are distributed horizontally and diffused outwardly during the process of rock uniaxial compression. In the pillar retention mining process, the stress flow vectors in vertical direction are larger than those in horizontal direction,and the stress flows in vertical direction mainly point from the roof and floor strata to the middle coal seam, while the stress flows in horizontal direction mainly point to the front of the mining face. When the excavation distance increases, the stress gradient near the mined out areas increases significantly, and the distribution of the stress flow vectors moves forward with the mining face.Through the uniaxial compression test, it is found that the stress flow vector directions are consistent with the failure and deformation directions of the rock sample, which preliminarily demonstrates the internal correlation between the stress flow and rock failure. Finally, the monitoring and analysis method of stress flow in engineering site was discussed. The research work is expected to provide an intuitive cognitive form and a practical theoretical tool for the quantitative evaluation of coal bump risk and formulation of differentiated prevention and control measures.