As part of the work, studies of the rock’s permeability to gases were carried out using the original measuring apparatus, which makes it possible to study gas seepage through a porous medium under confining pressure conditions corresponding to in situ. Samples of selected sandstone, sapropelic coal, marble, granite, limestone, and spongiolite rocks were used for permeability studies. The permeability of these rocks was determined in relation to helium (He) and carbon dioxide (CO2) in various values of the confining pressure: 1, 5, 10, 15, and 30 MPa. The obtained variability ranges of permeability coefficients allowed to assign the tested samples to particular classes, from poor and tight permeable rocks, where k∞ < 1 mD and k∞ < 0.1 mD (granite, marble), through good permeable rocks with a value of 10 < k∞ < 100 mD (limestone, spongiolite, sandstone), to very good permeable rocks with coefficient k∞ > 100 mD (coal). The Klinkenberg slippage effect was twice as large for He compared to CO2, and as permeability increased, the slippage effect disappeared. The Walsh model was used to analyze the obtained results, based on which it was found that the highest impact of effective stress was observed for a granite sample, the smallest for sapropelic coal, where an increase in effective stress by about 30 MPa reduced the permeability of coal to He by 50% and to CO2 by 30%. Changes in the structural properties of rocks as a result of subjecting them to gas seepage processes under confining pressure conditions were also examined. Open porosity, specific surface area, pore size distribution, and mean pore diameter in the samples were determined. In most of the studied rocks, a decrease in porosity and a reduction in the pore space of the rocks were observed after permeability tests under confining pressure conditions.