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The impact of faults on the contemporary stress field in the upper crust has been discussed in various studies. Data and models clearly show that there is an effect, but so far, a systematic study quantifying the impact as a function of distance from the fault is lacking. In the absence of data, here we use a series of generic 3-D models to investigate which component of the stress tensor is affected at which distance from the fault. Our study concentrates on the far field, located hundreds of metres from the fault zone. The models assess various techniques to represent faults, different material properties, different boundary conditions, variable orientation, and the fault's size. The study findings indicate that most of the factors tested do not have an influence on either the stress tensor orientation or principal stress magnitudes in the far field beyond 1000 m from the fault. Only in the case of oblique faults with a low static friction coefficient of μ=0.1 can noteworthy stress perturbations be seen up to 2000 m from the fault. However, the changes that we detected are generally small and of the order of lateral stress variability due to rock property variability. Furthermore, only in the first hundreds of metres to the fault are variations large enough to be theoretically detected by borehole-based stress data when considering their inherent uncertainties. This finding agrees with robust stress magnitude measurements and stress orientation data. Thus, in areas where high-quality and high-resolution data show gradual and continuous stress tensor rotations of >20° observed over lateral spatial scales of 10 km or more, we infer that these rotations cannot be attributed to faults. We hypothesize that most stress orientation changes attributed to faults may originate from different sources such as density and strength contrasts.