Squeeze-film damping on microresonators is a significant damping source even when the surrounding gas is highly rarefied. This article presents a general modeling approach based on Monte Carlo (MC) simulations for the prediction of squeeze-film damping on resonators in the freemolecule regime. The generality of the approach is demonstrated in its capability of simulating resonators of any shape and with any accommodation coefficient. The approach is validated using both the analytical results of the free-space damping and the experimental data of the squeeze-film damping on a clamped-clamped plate resonator oscillating at its first flexure mode. The effect of oscillation modes on the quality factor of the resonator has also been studied and semi-analytical approximate models for the squeeze-film damping with diffuse collisions have been developed.