Annular seals serve an important role in the dynamics of turbomachinery by reducing leakage of a process fluid while also contributing potentially destabilizing forces to the rotor system. Hole-pattern seals have been the focus of many investigations, but recent experimental studies have shown that there are still many phenomena that require exploration. One such phenomenon is the influence of hole depth on the static and dynamic characteristics of the seal. In this paper, a hybrid computational fluid dynamics (CFD)/bulk-flow method is employed to investigate the nonmonotonic relationship between hole depth and leakage shown in experimental measurements of a hole-pattern seal by Childs et al. (2014, “The Impact of Hole Depth on the Rotordynamic and Leakage Characteristics of Hole-Pattern-Stator Gas Annular Seals,” ASME J. Eng. Gas Turbines Power, 136(4), p. 042501). Three hole depths (1.905 mm, 3.302 mm, and 6.604 mm) and three running speeds (10,200 rpm, 15,350 rpm, and 20,200 rpm) are considered. For the steady-state flow, the 3D Reynolds-Averaged-Navier-Stokes (RANS) equations are solved with the k-ϵ turbulence model for a circumferentially periodic sector of the full seal geometry. The steady-state results are input into the first-order equations of a bulk-flow model to predict rotordynamic coefficients. Results of the hybrid method are compared to experimental data. CFD predicted leakage showed good agreement (within 5%) for the 3.302 mm and 6.604 mm hole depth configurations. For the 1.905 mm hole depth seal, agreement was within 17%. An additional set of calculations performed with the shear stress transport (SST) turbulence model produced worse agreement. Examination of streamlines along the seal show that the hole depth controls the shape of the vortex that forms in the hole, driving the resistance experienced by the jet flow in the clearance region. For the rotordynamic coefficients, good agreement is shown between predictions and experiment for most excitation frequencies.