AbstractUnderstanding deformations and fluid flow in fractured rocks is of central importance for many subsurface flow applications. Thus, numerical frameworks are needed that capture the coupled mechanical and hydraulic behaviour, including scenarios with complex fracture networks. This paper employs the extended finite volume method to represent fracture manifolds in a poroelastic matrix domain and to compute shear and tensile displacements of fracture segments. However, using embedded fractures with non‐conforming grids can lead to severe convergence issues while computing shear slip and tensile opening of intersecting and parallel fractures, particularly if they have similar slopes. Our proposed solution of this problem is to slightly deform the fracture geometry by merging critical segments. We discuss and show examples of which attributes the merged segment has to adopt to ensure the correct slip behaviour at an intersection. Thereby it is crucial that the flow topology remains unaltered. Analysing failures of kinked fractures and fracture intersections show the flexibility of the devised algorithm. Moreover, it is demonstrated that deformation and opening patterns of a natural network with more than 200 fractures are qualitatively predicted very well. This method is a simple solution to treat multiple fracture segments in a grid cell, hence it can be used for any model embedding fractures in non‐conforming grids.