A new model for the determination of the permeability in sandstones under confining pressure is presented. Building on the concepts of digital rock physics, a numerical model is derived from a 3D tomographic scan. The pressure-dependent behavior is mimicked by adding an artificial flow resistance to the pore throats. All permeability simulations are performed using an in-house finite-volume code. In the first step, the proposed model is tested based on a given Bentheim sandstone sample and compared with experimental data. In the second step, the influencing factors of the model are investigated. Mainly discussed are the influences of the tomographic scan and the numerical resolution. Overall, the proposed model is observed to be capable of reproducing general trends of the experimental data, whereby the magnitude of the numerically determined permeabilities can strongly depend on the investigated influencing factors.