We present a simulation technique to predict tool influence functions (TIFs) based on the Precessions polishing process, which is driven by addressing mass fabrication of the European Extremely Large Telescope mirror segments. Precessions polishing requires accurate and predictable TIFs to optimize the multiple process parameters, particularly when sequential polishing runs are performed by different polishing tools. In this paper, the static and dynamic TIFs are simulated based on the Preston equation. The velocity distribution is calculated according to the geometry of the precession motion. The pressure distribution at the polishing spot is calculated by means of finite element analysis (FEA). The FEA result is validated by direct force measurement with a simulation error of 4.3%. The simulation results of TIFs are verified by an experiment that shows the residual errors are less than 5% for both static and dynamic TIFs.