Abstract: Compared with cylindrical gear transmission, face gear transmission has good transmission performance, light weight and high load capacity, with good economic and technical benefits. However, the inner radius of face gear will have undercut phenomenon, application and popularization of restricted face gear. In order to get the theory of accurately solve minimum inner radius of face gear. This article according to the gear shaper machining process of the orthonormal face gear and the theory of gearing derived the working tooth surface equation and the transition surface equation of the orthogonal face gear, and the curve equation of undercut boundary line. Through the solution and analysis of curve equations of undercutting boundary line, get the key point coordinate position of no undercutting, and then get the calculation formula for minimum inner radius of orthogonal face gear. In the MATLAB software on working tooth surface equations, transition surface equation and undercut boundary line equation to carry out parameter discretization, and carry out visual generation and simulation analysis, Verify the correctness of the theory method for accurately solve minimum inner radius of face gear described in this paper.