Abstract: An optimization system for fir tree root is developed for design layout of the fir tree joint area in gas turbine so as to decrease the weight of aero engine and shorten the design cycle.This system is suitable to design the 2￣5 pairs of teeth used in modern aero engines.After the optimization the smallest weight subject to the static strength constraints has been attained,the FEM is used to check the distribution of stresses,particularly the concentration stress,and the results are shown on the screen for making decision.