This paper presents numerical results for a hydraulic fracture interacting with a frictional geological discontinuity in layered sedimentary rocks. A 2D hydraulic fracture model has been developed that can consider the details of the interaction and includes elastic rock deformation coupled to both fluid flow and frictional slippage. The interaction can result in fracture blunting, crossing or entering the interface, depending on modulus and stress contrasts, as well as the shear strength of the discontinuity. The numerical results are compared to experimental and field observations. When hydraulic fractures interact with long geological discontinuities, fracture growth can be stopped or retarded by the process. Treating pressure is increased by the large pressure gradients generated at offsets in the fracture path. Proppant transport can be impeded by such offsets because of the associated narrowing of fracture width. In some cases, the hydraulic fracture cannot easily enter frictional discontinuities when the interfaces have low frictional strength. In addition, pre-existing flaws are likely to serve as sites for re-initiation, allowing further hydraulic fracture growth into the intact side of the discontinuity. A higher closure stress acting in the intact rock favors arrest of the hydraulic fracture at the discontinuity, e.g., when a fracture attempts to cross a soft-to-stiff bedding plane. As a part of the interaction, the main hydraulic fracture will typically also lose fluid into cross-cutting frictional discontinuities.