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This paper deals with theory and computation of fluid flow in fractured rock. Non‐Darcian flow behavior was observed in pumping tests at the geothermal research site at Soultz‐sous‐Forêts (France). Examples are examined to demonstrate the influence of fracture roughness and pressure‐gradient dependent permeability on pressure build‐up. A number of test examples based on classical models are investigated, which may be suited as benchmarks for non‐linear flow. This is a prelude of application of the non‐linear flow model to real pumping test data. Frequently, conceptual models based on simplified geometric approaches are used. Here, a realistic fracture network model based on borehole data is applied for the numerical simulations. The obtained data fit of the pumping test shows the capability of fracture network models to explain observed hydraulic behavior of fractured rock systems.