Abstract: Longitudinal grooving hydraulic fracturing is a kind of pressure relief technology for roadway cutting under strong dynamic pressure. The core is to control the cracking and propagation direction of cracks. However, the cracks are usually deflected under the influence of the maximum principal stress after directional fracturing. The propagation direction of the crack is related to various factors such as in-situ stress conditions, grooving angle, pump flow rate and rock mechanical properties. Research on the crack deflection law under the influence of multiple factors of longitudinal groove hydraulic fracturing is carried out to provide a reference method for the construction design of longitudinal groove hydraulic fracturing drilling. The XFEM module in ABAQUS software was used to establish the two-dimensional model of longitudinal grooving hydraulic fracturing. The feasibility verification of the numerical model was achieved by comparing with the previous physical test results of longitudinal grooving hydraulic fracturing, and then the large-scale longitudinal grooving hydraulic fracturing model was established, and the fracture deflection law of longitudinal grooving hydraulic fracturing under the condition of coal mine roof sandstone was studied in detail. The results show that the horizontal stress ratio is an important factor affecting the crack deflection distance. When the vertical principal stress is 10 MPa, the minimum horizontal principal stress is 6 MPa, and the horizontal stress ratio increases from 1.5 to 3.5, the crack deflection distance decreases by 55.3%, 56.9% and 41% respectively. The cutting angle has a great influence on the crack propagation path and a relatively small influence on the crack deflection distance; When the horizontal stress ratio is 1.5 and 2.0, the crack deflection distance increases continuously and has a large increase range when the pump flow increases from 30 L / min to 180 L/min. When the horizontal stress ratio is 2.5, the growth rate of the crack deflection distance is significantly reduced; When the horizontal stress ratio is 1.5, 2.0 and 2.5，respectively, the crack deflection distances corresponding to the pump flow of 90 L / min are 4.05m, 1.81m and 0.75m respectively. A large increase in the deflection distance can be achieved by greatly increasing the pump flow. The study provides significant reference for the selection of flow rate of longitudinal grooved hydraulic fracturing pump and the determination of borehole spacing under different conditions.