Abstract—Numerical modeling of induced seismicity resulting from fluid injection into the subsurface is considered. One of important factors determining the slip dynamics of a tectonic fault during fluid injection loading is the form of the law of friction acting on the fault sides. The numerical analysis in the context of a slider model compared to the results of laboratory experiments has shown that a two-parameter rate-and-state friction law describes the widest spectrum of the observed sliding modes. A double porosity model and a slider model for fracture are used to simulate the induced seismicity in the region of Basel, Switzerland, caused by geothermal stimulation. A physically complete model of embedded fractures which allows for calculating fluid flow in a rock with fractures or faults taking into account changes in the hydraulic properties of the latter is presented. Fault deformation process is described based on the displacement discontinuity method. Based on the model, the results of the field experiment on water injection into a fault in the southern France are analyzed. The development of fault slips is studied as a function of a number of parameters characterizing a fault, filtration properties of a rock, and injection pattern. The conditions for the emergence of seismic slip in the context of the proposed model are established.