The study investigated how variations in pressure ratio affect the leakage flow of a brush seal for both contact and clearance structures, in which the clearance is measured as the distance between the bristles tip and the rotor surface. This investigation utilized the Reynolds-Averaged-Navier–Stokes (RANS) equations alongside a two-dimensional axisymmetric anisotropic porous medium model. To verify the model’s accuracy and dependability, the obtained results were compared with previous numerical results and experimental observations, showing a satisfactory level of agreement. The results indicate that the predominant pressure drop occurs downstream of the bristle pack with the clearance model exhibiting a higher leakage rate compared to the contact model. Leakage increases proportionally with the pressure ratio, while axial velocity gradually rises and radial velocity experiences a significant increase. In conclusion, the leakage in the brush seal contact structure is significantly lower than in the clearance structure, resulting in the best performance.