It is well known that in many cases rock permeability depends upon in situ stress conditions and on the pressure of the flowing fluid. Parallel and quasi-parallel joints represent one of the most often observed permeability structures. Frequently, joint sets are closely spaced and although joint mechanical interaction could significantly affect their aperture, the interaction is usually ignored in the evaluation of permeability. In this paper, on the basis of accurate computations of the interaction between the parallel fractures and conducted physical experiments, we suggest that the internal pressure can, in fact, close the pressurized joints. In general, there is a critical spacing between the parallel fractures below which their surfaces start contacting under the extensional load. However, the two edge fractures (end members) in the set remain widely open because they are not suppressed from one side. These effects dramatically change rock permeability and the fluid flow pattern.