Aiming at the phenomenon of undercut in the process of circular arc tooth profile face gear,by using the research method combining theoretical analysis,numerical calculation and simulation experiment,the minimum inner radius of the face gear without undercut is studied. Firstly,the tooth surface equation of the tool gear is established,and the working tooth surface and the transition surface equation of the gear are deduced from the combination of the tool and the circular arc tooth profile. And then according to the circular arc tooth profile face gear does not produce undercut conditions theory,through the MATLAB software to write the program for numerical calculation. The calculated results are compared with the results obtained by the simulation experiments,and the correctness of the minimum radius values of the circular arc tooth profile face gear without rooting is verified.