The effective pressure sensitivity of gas flow through two shales (Bowland and Haynesville shales) and a tight gas sandstone (Pennant sandstone) was measured over the typical range of reservoir pressure conditions. These are low permeability rocks such as can be exploited as caprocks above reservoirs that might be developed to store compressed air, methane, hydrogen or to bury waste carbon dioxide, all of which may become important components of the forthcoming major changes in methods of energy generation and storage. Knowledge of the petrophysical properties of such tight rocks will be of great importance in such developments. All three rocks display only a small range in log10 permeability at low pressures, but these decrease at dramatically different rates with increasing effective pressure, and the rate of decrease itself decreases with pressure, as the rocks stiffen. The pressure sensitivity of the bulk moduli of each of these rocks was also measured, and used to formulate a description of the permeability decrease in terms of the progressive closure of narrow, crack-like pores with increasing pressure. In the case of the shales in particular, only a very small proportion of the total porosity takes part in the flow of gases, particularly along the bedding layering.