A new approach for performing numerical direct simulation Monte Carlo (DSMC) simulations on turbomolecular pumps in the free molecular and transitional flow regimes is described. The chosen approach is to use surfaces that move relative to the grid to model the effect of rotors and stators on a gas flow. The current article describes the method and compares the results to experimental and theoretical data by Sawada [Bull. JSME 22, 362 (1979)]. The agreement between our results and Sawada's results are excellent.