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The interaction between hydraulic fractures (HF) and natural fractures (NF) is one of the most fundamental phenomena in hydraulic fracturing. The near-wellbore interaction between HF and NF significantly affects fracking-related operations including the injected fluid flow, proppant transport and well productivity. However, the nature of fracturing modes, combined with hydro-mechanical coupling, poses great difficulties and challenges in addressing this problem. Literature review suggests that little research has been undertaken on near-wellbore interaction, especially considering the fully coupled hydro-mechanical mixed-mode fracturing process. This paper develops a new fracture model incorporating the Mohr–Coulomb criterion with the cohesive crack model. The model is implemented into ABAQUS solver by in-house FORTRAN subroutines. The rock matrix and cohesive crack interfaces are both coupled with fluid flow. The developed model is then validated by comparing the results with analytical solutions and experimental results. Moreover, the effects of approach angle, NF location, in situ stress, cohesion strength and friction angle of NF, and flow rate on the near-wellbore interaction are investigated. Three interaction modes, i.e., cross, deflect and offset, are reproduced through the numerical method. The crack deflection into NF is a shear-dominated mixed-mode fracture. A high injection pressure in the wellbore tends to drive the HF to cross a NF located close to the wellbore. The smaller the cohesion strength and friction angle of NF is, the larger the offsetting ratio is. A low injection flow rate can help activate natural fractures near the wellbore when intersected by HF.