Usually machine geometry precision design is preformed depending on human experience but not reference data form design theory. To learn numerical effect an approximate model of relationship between machine geometry precision and product machining precision is provided based on multibody theory. The analysis results by Monte Carlo sampling would deduce geometry precision of each axis in machine. Taking geometry precision design of spiral bevel gear milling machine as an example, the approximate model well explains effect of machine geometry error on gear product surface machining quality by explicit. Then geometry precision of each axis is obtained by mapping from tooth surface machining precision.