Determination of original state of stress in rock mass is a very difficult task for rock mechanics. Yet, original state of stress in rock mass has fundamental influence on secondary state of stress, which occurs in the vicinity of mining headings. This, in turn, is the cause of the occurrence of a number of mining hazards, i.e., seismic events, rock bursts, gas and rock outbursts, falls of roof. From experience, it is known that original state of stress depends a lot on tectonic disturbances, i.e., faults and folds. In the area of faults, a great number of seismic events occur, often of high energies. These seismic events, in many cases, are the cause of rock bursts and damage to the constructions located inside the rock mass and on the surface of the ground. To estimate the influence of fault existence on the disturbance of original state of stress in rock mass, numerical calculations were done by means of Finite Element Method. In the calculations, it was tried to determine the influence of different factors on state of stress, which occurs in the vicinity of a normal fault, i.e., the influence of normal fault inclination, deformability of rock mass, values of friction coefficient on the fault contact. Critical value of friction coefficient was also determined, when mutual dislocation of rock mass part separated by a fault is impossible. The obtained results enabled formulation of a number of conclusions, which are important in the context of seismic events and rock bursts in the area of faults.