<p>The volumetric error of five-axis machine tools (FAMTs) is significantly influenced by geometric errors arising during multi-axis interpolation. These errors are primarily determined by manufacturing and assembly tolerances. The large number of tolerance parameters poses significant challenges to accurately identifying the key error contributors. This study proposes a method to identify critical tolerances for volumetric error in FAMTs using multi-body system modeling and sensitivity analysis. The model accounts for all geometric errors, and establishes a mapping between tolerance parameters and geometric errors. Furthermore, the machining workspace is discretized into a grid to quantify the influence of each tolerance parameter. Simulation results show the key tolerances influencing volumetric error are relatively concentrated. It is validated by machining a standard inspection workpiece on a FAMT. The average improvement in critical precision indicators for the workpiece was measured at 22.93%. This work effectively identifies the key tolerance parameters affecting the volumetric error of FAMTs. It provides a practical technical approach for enhancing machining tool accuracy, as well as guiding design and assembly.</p>