A 3D Monte Carlo (MC) simulation approach is developed and employed to study the effect of the oscillation mode on the squeeze-film air damping in the free-molecule regime. By tracking individual gas molecule's motion and its interaction with the resonator, the MC approach is by far the most accurate modeling approach for the modeling of squeeze-film damping in the free-molecule regime. The accuracy of this approach is demonstrated on several cases in which either analytical solutions or experimental measurements are available. It has been found that unlike the case when resonators oscillate in an unbounded domain, squeeze film damping is very sensitive to the mode shape, which implies that some of the existing modeling approaches based on rigid-resonator assumption may not be accurate when applied to model resonators oscillating at their deformed shape.