The spatio-temporal changes of the stress state in a geothermal reservoir are of key importance for the understanding of induced seismicity and planning of injection and depletion strategies. In particular the poro-elastic effects on the stress state due to re-injection or depletion of water are of interest for both geothermal projects and hydrocarbon exploitation. In addition to the conventionally used effective stress concept, poro-elasticity affects the stress tensor components differently as a function of changes in pore pressure. Here, we provide an analytical base for the long-term changes of the 3D stress tensor components as a function of pore pressure changes. Results indicate that for a constant rate of injection or depletion the coupling between pore pressure and all stress tensor components depends on the location in the reservoir with respect to the re-injection/depletion point as well as the time since the beginning of pore pressure changes. Our systematic analysis suggests that poro-elastic stress changes can even locally modify the given tectonic stress regime. Furthermore, the results predict that localized changes of maximum shear stress can lead to different fracture orientations than those expected when poro-elastic effects are not considered. These results indicate a need for 3D geomechanical-numerical studies of more realistic reservoir settings in order to study the 3D effects of pore pressure/stress coupling. Our generic 3D geomechanical-numerical study shows that less than two years of production of a single well changes shear stresses by 0.2 MPa. Thus, in reservoirs with decades of production shear stress change can reach sufficiently high values to re-activate pre-existing faults or even generate new fractures with unexpected orientations.