Hydrocarbons reservoirs are dynamic systems that constantly changes during depletion. The production of fluids from a reservoir often reduces pore pressure such that there is an increase in its effective stresses. This may cause compaction which, in turn, may impact matrix permeability. On the other hand, during water injection on reservoirs, the pore pressure increases and effective stress decreases. An understanding of these changes is of fundamental importance to performance predictions and management of the stress- sensitive reservoirs. The main objectives of this work is to experimentally investigate the stress dependence of rock producing oil permeability, its anisotropy and hysteresis under hydrostatic and true triaxial stress conditions. In the present investigation a new true triaxial equipment, one that is able to apply the three principal boundary stresses independently using cubic samples was utilized. This equipment can apply a realistic stress state to the rock samples for measuring of the relevant properties under stress states that mimic the in situ condition. The experimental results have produced evidence that hydrocarbon production and reserve estimates may significantly improve when permeability is considered as a dynamic variable. Permeability in all three formations (Berea, Rio Bonito and Botucatú sandstones) was shown to be strongly stress-dependent both under a hydrostatic stress state and under a true triaxial stress state. Nevertheless, the effect of stress states on permeability has clearly shown that permeability reduction under true triaxial stresses was less than that under hydrostatic stresses.