This paper deals with the unsteady gas filtration through a granular layer attached to a rigid end-wall when impacted head-on by a weak shock wave in a shock tube. The main goal of the present work is to study the gas pressure field developed inside the granular layer during its compression by the shock wave. A physical model is proposed for simulating the phenomenon and solved numerically. The numerical results are compared with the measured gas pressure at different locations inside the sample and at the end-wall covered by the granular layers. Good agreement is found between the calculated gas pressure signals and those measured at the shock tube end-wall covered by a granular layer at the final stage when the gas pressure is mostly governed by gas filtration. In the initial, unsteady part of the signals, large deviations exist between the calculated and the experimental results. The only reason for the agreement or discrepancy between the theoretical predictions and the experiments is the compaction effect associated with the formation of the gas pressure profile at the shock tube end-wall covered with a granular layer.